It's not about their actual physical fitness and combat abilities relative to each other so much as their relative enthusiasm for these things.
If the guy and girl possess personality traits that either a masculine woman or a feminine boy have, they fit.
The masculine girl does not have to be a tomboy to fit this, and the feminine boy does not have to be Ambiguously Gay to fit this either.
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It is quite possible to spot this when the guy has a pink product, while the girl has the same one in blue.
Anime, Manga, and Manhwa
Akira and Mizuki from Mayu Shinjo's Ai Ore! Love Me!play around this. Akira is feminine-looking and the "princess" of his all-boys school, while Mizuki is androgynous and the "prince" at her all-girls school. However, personality-wise Akira is quite dominant and masculine and Mizuki isn't really all that boyish — though in the counted times she does show a more assertive side, Akira isn't that displeased either.
Predated and played straighter (so to say) by Kazuto "Towa" Sakuma and Miya from Sensual Phrase. Kazuto's a very girly-looking rock musician who dresses as a female even off-stage, Miya is the Bifauxnen beautician who both dates him and created his androgynous looks.
Deunan and Briareos from Appleseed could possibly count, except that Briareos is a hulking cyborg four times the size of Deunan. But their relationship follows the trope pretty straight.
Baka to Test to Shoukanjuu with the identical twins Yuuko (masculine girl) and Hideyoshi (feminine boy) Kinoshita. While Yuuko is typically feminine in traits (such as being good at cooking), her personality fit this trope because of her aggressive, prideful, arrogant, quick-to-anger, and competitive behavior. Hideyoshi on the other hand is calm, helpful, and supportive. Ironically, he is also much more popular than Yuuko, much to her dismay, because of hislooks.
Although there are signs of it in the book and movie, Sakura Ogawa and Kazuhiko Yamamoto's relationship is shown to be like this in the manga of Battle Royale.
Ranmaru and Tsuwabuki from Binbo Gami Ga aren't a couple (although Ranmaru wishes they were) but their dynamic fits this trope well. Tsawabuki is the dutiful Promoted To Parent big brother to his four younger siblings, he is skilled at domestic chores and is pretty even-tempered. Ranmaru is the ridiculously Hot-BloodedBorn in the Wrong CenturyHeir to the Dojo girl. Its not that Tsuwabuki is not manly but that Ranmaru is significantly MORE manly. Case in point, number of girls in their class in love with Tsuwabuki? 3. With Ranmaru? Pretty much all the rest!
Black Lagoon: Revy swears like a sailor, chugs rum, collects guns, and has no problem jumping onto a moving boat and killing every hostile on it, by herself, like an Action Hero. In the first arc, she was about to put Rock in a dress and hairbow because he seemed so feminine in contrast; the sensitive one who wants to talk things out without anyone getting hurt.
Chrono and Rosette in Chrono Crusade have elements of this. Chrono is implied in both versions to be better with housework (in the manga he's shown in an apron at one point, and in the anime the Elder says he does the cooking and cleaning for him), and is much more meek and gentle (although has an extreme Berserk Button, often putting him into an Unstoppable Rage), while Rosette is loud, brash, swears constantly and was a Lethal Chef as a child. They both have their moments where they act more stereotypically like their genders (Chrono is very protective of Rosette, and Rosette is very fond of pretty dresses), but they still don't fit neatly into gender roles.
Played up early on in Claymore between Clare and Raki, where Clare is the badass lone wolf from a mercenary organization sent to hunt demons, while Raki was the "damsel in distress" whom she rescued, and who then needed her companionship so traveled with her and made himself useful by cooking for her. This slides off later on as Raki starts learning the ways of combat, though does not disappear entirely.
Re-L Mayer and Vincent Law from Ergo Proxy; Vincent is easily more emotional while Real is usually expressionless, impatient, or angry.
Sora and Yukari from Family Compo are a married transsexual couple. Here is what they look like the one time they dress accordingly to their birth gender. Here is what they look like dressed to their own liking.
Hayate the Combat Butler has the title's Hayate Ayasaki being extremely polite, humble, and skilled at domestic tasks. Mirroring him is pink-haired swordswoman Hinagiku Katsura (one of his Love Interests) who is assertive, highly-athletic, and projects an aura of leadership. Simply put, he can make women around him feel their femininity is being challenged and she is cooler than any of the boys at school resulting in most of the guys andgirls crushing on her.
Each of them is a mix of traits however, and Character Development has resulted in them evening out somewhat. Hinagiku becomes less "tomboy" and more "girly", by showing that she is just as good a cook as master-chef Hayate and adores cute things, as well as focusing on her romantic side. Hayate gets to show off his determination and combat ability in addition to his dedication to duty and fulfilling his promises. Notably, he seems to like her "boyish" traits and Imagine Spots from her show that she kinda likes his "girlish" side as well.
Haruka and Kotake from Himitsu Kichi one-shot My Own Secret. She's a boyish Bifauxnen who practices judo and he's a feminine guy who likes cooking and sewing.
Infinite Stratos has the biggest BadassAce Pilot Chifuyu Orimura living with her little brother and main protagonist Ichika Orimura for the majority of their lives. He is the series House Husband who takes care of all the housework while she earns the money for both of them.
A non-romantic example (not counting Aoi's one-sided crush on her) is Misaki and Aoi from Kaichou Wa Maid-sama!.
Sumire and Momo from Kimi Wa Petto. Sumire is an efficient, successful journalist who watches pro wrestling and Sentai anime in her spare time and is a martial arts master on the side, while Momo is a modern dancer who is fairly emotional and doesn't mind taking on the role of Sumire's pet.
Chips (masculine-looking female) and Nachos (feminine male) from Magical Nyan Nyan Taruto. They fit this more in their appearances (especially Nachos), although Nachos is definitely the more sensitive and kinder of the two.
Akira Okuzaki and Mai's little brother Takumi Tokiha from Mai-HiME.
Mako-chan and Touma from Minami-ke. Makoto isn't girly per se, but most of his scenes alongside the tomboy Touma feature him masquerading as a girl. In one episode, he also describes masculine and feminine traits inherited from his mother and father, respectively.
Mobile Suit Gundam 0083: Stardust Memory has Mora Bascht and Chuck Keith. Although Chuck isn't all that girly, he's a fairly unassuming guy, and Mora is pretty Amazon (and head and shoulders taller than him), so this vibe is definitely present.
Little My (Masculine Girl) and Sniff (Feminine Boy) from The Moomins are a non-romantic example of this.
The second of these, Konatsu, is so feminine thanks to years of brutal treatment that he can almost be argued as transsexual, to the point that his reaction when surprised in a bath is to squeal like a girl and cover his non-existent breasts.
Ranma Saotome and Akane Tendo can be seen as a zigzagging example of this. Akane is a notoriously short tempered and violence-pronetomboy, infamous for her total lack of cooking skill, horrible at anything arts and craftsy (such as making cookie shapes, sewing, painting, etc), and not terribly good at housework. Ranma, in contrast, is capable of acting much more feminine, is very good at cooking and sewing, hates mess to the point he once forgot about burglaring a flat to clean up the mess inside instead, can actually turn into a girl more or less at will, and, according to one post-series book, actually has developed a secret enjoyment of crossdressing by the time the series ends, thanks to all the times he dressed up as a girl for whatever Zany Scheme he was pulling. On the other hand, Akane desperately wants to be more feminine and tries her hardest to achieve that, as well as having stereotypically "girly" fears (such as loathing ghost stories) and a rather idealised view of femininity (due to her beloved mother's early death andhaving been partially raised by her Yamato Nadeshiko older sister Kasumi), while Ranma is a macho jock-type who'll even go around near-naked in female form because he's that masculine.
Andre Grandier and Oscar Francois de Jerjays from Rose of Versailles. Perhaps not a textbook example, since Andre is not tremendously effeminate. But Andre is the more sensitive and people-oriented one, while Oscar is very direct and more goal oriented. Oscar is referred to as the "light," and Andre as the "shadow."
Genjou Sanzo & his new best friend Sharak Sanzo from Saiyuki are two peas in a pod. They're a mirror reflection of eachother, except for appearance. Sanzo is short, was mistaken for a girl a lot as a kid, is teasingly referred to as "princess," wears a long flowing garment, & is the weakest guy in his party. Sharak has barely noticeable breasts, wears men's monk robes, is very buff, is covered in scars, & talks & carries herself in a masculine manner, plus she does not like being thought of or looked at at as a woman.
Ryuji and Taiga from Toradora! have aspects of this in personality, but it contrasts with their appearance. Taiga is small ("looks like a doll") but has a brash, loud and angry personality. Ryuji has the Face of a Thug but is generally quiet and enjoys housework (especially cleaning but also cooking).
Ryunosuke from Urusei Yatsura was unwillingly raised to be the ultimate manly man by her father, and later discovers she's in an Arranged Marriage with Nagisa, the ghost of a guy raised to be ultra womanly. Though after coming back to life, he turns out to also be insanely strong, despite mostly hiding it behind over the top girly behavior.
Jung Suk Ha and Park Bong Bin from Utopia Of Homosexuality are respectively a Butch Lesbian and a Camp Gay who eventually end up together. Yes, a very misleading title.
Ito and Makoto from W Juliet. So much that it's even implied that they'll get married in drag!
Shuichi Nitori and Yoshino Takatsuki, the adolescent protagonists in Wandering Son, each prefer things associated with the opposite gender. If you think of them as their desired sexes, then this is inverted as Pink Girl, Blue Boy ... then slightly inverted again when you notice Takatsuki has pink hoodies. The anime really likes to throw around pink and blue, especially for the Nitori siblings.
Your And My Secret features a soft-spoken boy, Akira Urehara and loud-mouthed girl Nanako Momoi being Body Switched into one another's bodies. Just about everyone notices how much more masculine Akira and how feminine Nanako has become, and approve.
Betty and Archie, from the main series, Depending on the Writer. When Archie's car breaks down, Betty fixes it. And there is even one comic where they try to enter a team surfing competition, but since Archie is too weak to carry Betty, Betty carries Archie.
Samantha and Bingo from That Wilkin Boy are Expies of Betty and Archie who fit even better. Samantha is physically very strong, while Bingo is a weak musician. This trope may explain why her father never succeeded in breaking them up or getting her to date a manlier man.
This gets played with sometimes with Moose and Midge. While Moose normally exhibits standard jealous male behavior in regards to his girl, it is often suggested that Midge wears the pants in their relationship.
Possibly Redlance and Nightfall from ElfQuest, although the elves don't quite go for the same kind of gender stereotyping that humans do. More to the point, the siblings Suntop and Ember. When trying to get a studio to do an animated version of the comic, Executive Meddling said that you can't have a calm guy and a tomboyish girl, and this is one of the reasons the author quickly abandoned that studio.
The New Gods Mister Miracle (escape artist and acrobat from New Genesis) and Big Barda (renegade Apokaliptian gladiator) are in many ways a Happily Married version of this.
Sin City has a non-romantic variation of this in Dwight and Miho. Dwight is a laid-back everyman while Miho is much more violent and dangerous (which is definitely saying something when you take Dwight's own penchant for violent protectiveness into consideration). In fact, Dwight has expressed fear of Miho in the past and worked to ensure that he didn't piss her off.
Dale and Andrea from The Walking Dead. Dale's not feminine, but physically he isn't strong. Andrea is the sharpshooter, more energetic and take-charge personality.
Yorick and his love interest finally get together near the end of Y: The Last Man. He compares them to the main couple of Moonlighting (a UST-filled detective series starring Bruce Willis and Cybill Sheperd), but takes great care with specifying SHE is the Bruce Willis equivalent.
In the comic strip U.S. Acres, Orson the pig was the feminine boy, and Lanolin the sheep was the masculine girl.
The Bleach fanfic Chasing the Moon gives us a platonic version (that potentially overlaps with Vitriolic Best Buds). Karin and Yumichika are fourth and fifth seat of the Eleventh Division respectively, and Yumichika constantly bemoans the fact that she won't even try to be beautiful, while Karin just wants him to stop messing with her clothes. She's actually dating Toshiro, and they're not an example of this trope.
PJ and Beret Girl in An Extremely Goofy Movie have a lot of things in common, but they also have a few major differences in that Beret Girl is bold, aggressive, and flirtatious, while PJ is a timid, passive Insecure Love Interest. The couple invertsNo Guy Wants to Be Chased, as Beret Girl takes the lead at every step in their relationship and PJ enjoys this, but when Beret Girl was chased by Bobby moments before, she was disgusted. Beret Girl also has a significantly deeper voice than PJ, and is not much shorter, as well as going out of her way to protect him early on.
There was a short film featured on Logo that showed a Gender Flip of a heterosexual wedding. The bride wore a black pantsuit; the groom wore a white tuxedo and veiled top hat, and held the bouquet as his mother walked him down the aisle. He was also kind of short. Even among the wedding-goers, all the men wore different suits while the women were dressed more low-key.
In the movie Lover Come Back, Jerry Webster is emotional and intuitive, while Carol Templeton is logical and reserved. This is taken Up to Eleven when Webster pretends to be a chemist to trick her.
Star Wars give us a non-romantic and sibling example with Luke Skywalker and Leia Organa. Luke is a naive, sensitive farmboy who more or less fell into his role as Champion of the Rebel Alliance, while Leia is a stern, no-nonsense military commander who took charge of her own rescue mission.
At first sight, King Verence II and Queen Magrat from (among other novels) Lords and Ladies are more Feminine Boy, Feminine Girl. But when push comes to shove Magrat has Hidden Depths and can transform into an Action Girl. Verence's "hidden depths" came when he was made King and actually took an interest in his subjects and how to improve their lives with the latest advances in agriculture.
This is a central theme in the Annie M. G. Schmidt story Het Fornuis Moet Weg ("The Stove Has To Go"). It's about a girl who wants to become a carpenter, and a boy who wants to become a stay-at-home dad. They argue about it with grownups who are moving an old stove out of the house. Eventually, one of the grownups gets an idea: the stove can be seen as a symbol for the old times, when a lack of modern household appliances meant that work around the house took all day and gender roles stayed reinforced. Because of modern luxuries, women now actually have time to study and choose their own careers, so there shouldn't be a need anymore for gender roles to stay as they were. The story is considered a children's classic in The Netherlands.
Older Than Steam, even: in 1620 England, in response to a pamphlet entitled Hic Mulier, or The Man-Woman, which discussed the evils of women who dress and act like men, another pamphlet was published, Haec Vir, or The Womanish Man, stating that women would stop acting like men when men stopped acting like women.
There are elements of this in the relationship between Vin (a blunt Action Girl assassin) and Elend (a thoughtful, bookish nobleman) in Mistborn. It's not completely straight — Vin does have a girly side and Elend willget dangerous if sufficiently motivated — but the trope can definitely be seen here.
Pinky and Rex about a boy whose nickname was Pinky (his favorite color was pink) and Rex, a girl who liked dinosaurs and soccer.
In the Warhammer 40,000Ravenor novels, Patience Kys and Carl Thonius are described this way. Hyper intelligent, scholarly dandy Thonius is frequently referred to as a pussy, frequently by Patience herself, a vicious battle telekine. This might be entirely fair, as the novel mentions that anything short of an Astartes in full battle plate is a pussy compared to Patience Kys.
Jaime Lannister and Brienne of Tarth in A Song of Ice and Fire, aesthetically, at least. Jaime is said to be so handsome it spills over into "pretty" territory, while Brienne is known for her unattractiveness and her un-lady-like habits of wearing armor, wielding a sword, and beating the crap out people who piss her off. They form something of an uneasy Battle Couple in A Storm of Swords.
As people have observed, one of the fun things about them as a pairing is that they are very much a "beauty and the beast" couple... but which one is which changes depending on if you're talking about looks or about personality.
An additional example is a sibling pairing rather than a romantic one—Jojen and Meera Reed. Jojen is a frail, sensitive, and psychic boy, and Meera a physically inclined girl who protects him.
Another sibling dynamic, Theon and Asha also qualify.
In a very unusual setup for a Romance Novel, Nora Roberts' Tears Of The Moon has as its romantic leads Shawn, a sensitive songwriter and pub cook, and Brenna, a feisty, tomboyish handywoman.
The main couple in Elinor Glyn's Three Weeks have shades of this, at least in terms of gender roles — Paul is boyish but virginal, beautiful and compared to Sleeping Beauty, and the Lady is older, independent, mature, compelling and in charge.
Depending on the Writer, Mara Jade and Luke Skywalker. When Timothy Zahn writes them, Luke is the sweeter, gentler one who prefers to avoid violence when possible, is always giving second and third chances, and is very open emotionally. Mara is more hostile to the world, blunt and direct and not about to let herself be jerked around, much more fiercely independent, and untrusting.
By our standards, this is the default in the world of A Brother's Price. Men being so rare they are kept protected and secluded, and internalize a set of gender roles that encourage softness, vulnerability, passivity, physical attractiveness, and affinity for the domestic sphere, while women run the world and are just about universally more assertive, daring, and calculating. A little girl in tears over a cut on her knee is even told that big girls don't cry. By his world's standards, Jerin is actually rather feminine, as he works to escape when captured and does know how to ride horses, pick locks, read, and use a gun - although he's quite stricken when he actually fires it.
Avasrala from The Expanse series is a foul-mouthed, no-nonsense, tough alpha politician. Her husband is a gentle, philosophical academic.
Mortal Engines: Tom and Hester fit this trope, especially in the first half or so of the first book of the series. Hester hides her emotions, doesn't talk much, is a Bad AssAction Girl, and is used to dealing with the rough world beyond the cities without complaints. Tom, on the other hand, is sensitive, emotional, naive, and is constantly shocked by the rough-and-tumble world around him. As the series goes on Tom becomes tougher, while Hester sometimes shows quite a bit of her emotional side, so this trope isn't always in effect — though there are still parts in the later books where Tom very clearly fills the more traditionally "feminine" role in the story, with Hester acting "masculine." (For example, towards the end of Predator's Gold — for much of the book Tom seems to fit the "masculine" mold more so than Hester, but towards the end Hester becomes very protective of Tom, keeps him out of harm's way, and plays the macho action-hero while Tom fills a more sensitive and support-oriented role).
The two azi (roughly, clone servants) Florian and Catlin in Cyteen. Florian is sensitive, social, and a Friend to All Living Things, while Catlin is cold and militaristic. While they're both bodyguards, Catlin specialises in battle, whereas Florian is better at setting and disarming traps.
A non-romantic example in Little Women between Jo and Laurie — she's a no-nonsense, unmannered writer who feels uncomfortable in the presence of females, talks about her gender in a manner incredibly reminiscent of transgender people today, and finds sentimentality utterly repellent. He's an artist and a musician, is stated many times to have an acute sense for the beautiful, is initially (before his best friend stirs up his mischief and college gives him a gutter mind) described as always sweet and gentle, a hopeless romantic to the point of total despair when his heart is broken, and unfailingly sentimental.
Just to clarify: Yes, Jo is the girl and Laurie is the boy, and those are both nicknames of their own choosing.
In The Moomins, Little My (a tough and plucky tomboy) and Sniff (sensitive, cowardly and delicate) is a non-romantic example.
The Protector of the Small series has Kel- a stoic girl dedicated to becoming a knight and fighting injustice- and her friend Neal, a healer-turned-knight who often uses White Magic to help his friends and is constantly lovesick over court women.
Lee "Apollo" Adama and Kara "Starbuck" Thrace from the rebooted Battlestar Galactica are an interesting example of how to flip a gender dynamic: it's not so much about the way they look and dress as how they behave with each other. Apollo tends to be the softer, more introspective of the two, while Starbuck is louder, brasher, and more of an alpha than he is. Despite this, no one in-universe sees them as less masculine or less feminine for it.
Darlene and David from Roseanne spend the majority of their relationship with the gender roles filpped. When Darlene gets pregnant Roseanne even comments "I can't think of a better mother..than David."
In Carrusel, Valeria is louder, more outspoken, and has a stronger personality than her boyfriend David.
Chuck: Sarah and Chuck, even more so in the first two seasons before he Took a Level in Badass, but their personalities always fit. Chuck is the one who is in touch with his feelings, wants to talk things out, and can't stand to have fights unresolved. Meanwhile, Sarah is extremely guarded, tries to keep up a stoic front, hesitates to commit, and is always on the traditionally 'male' side of all their relationship-related arguments. Right down to Chuck being the one who wanted a big wedding.
In a nutshell, this is the relationship between the Fifth Doctor and Tegan Jovanka.
Newly married Amy Pond and Rory Williams seem to have this dynamic, as Amy is an Action Girl, while Rory is a bit of a Non-Action Guy and a nurse (and while male nurses are common these days, it's still a profession that's predominantly female where he comes from).
The Doctor lampshades it by referring to them as 'the Ponds' after their marriage, instead of 'The Williamses.' Rory doesn't seem very bothered by it. According to the Doctor, it's just because Amy has an awesome surname, but he still refers to Rory as "Mr. Pond." The series for its part leaves the question of whether Amy actually takes Rory's surname open until "Asylum of the Daleks" when she is shown signing a document as "Amy Williams" and it is later indicated that she uses the name Amelia Williams when she becomes a writer.
Not a couple, but Morgan Pink and Journey Blue are two soldiers who appear in "Into The Dalek". Mr. Pink (present day, earth) is now a math teacher and is rather sensitive because it's implied he killed at least one civilian and deeply regrets it. Ms. Blue (future, space) is still a soldier and is pretty gung-ho about killing Daleks especially since her brother died moments before she encountered the Doctor. In the end she asks if she can go with the Doctor and Clara. She could... if she hadn't been a soldier.
How I Met Your Mother does a lot of this: the men are sentimental, mild-mannered, reserved, romantic, blissfully domestic (Marshall) or kid-crazy (Ted), and are often made fun of for stereotypically feminine traits, while the women are tough, uncouth, uncultured, boisterous, insensitive, commitment-phobic (Robin, who was literally raised as her father's son, and allowed to join an all-boys hockey team), or sex-obsessed (Lily), and often engage in hypermasculine actions as comedy. However, Barney takes the aggressively-heterosexual male stereotype and drives it so far over the edge he overshadows everyone else.
However, Barney also gets his nails done and obsesses over clothing, making him feminine. And Lily is a soft-hearted romantic kindergarten teacher/artist who cries at the drop of a hat, whereas Marshall is a high-powered lawyer. So it's really played all over the place.
And then there is that one episode where they all realize that their partners are just like their parents, which has Marshall realize that Lily is just like his dad!
Possibly averted with Barney and Robin, as they often seem to be on level ground, as far as masculinity goes.
In Kamen Rider OOO, Shintaro Gotou is shown to be more compassionate and gentle than his female sidekick/assistant Satonaka, who hates sweets, can wield a gun with the best of them, and fights evil only because she is paid to do so.
Kamen Rider Wizard has the main character's two sidekicks: tough, gun-wielding policewoman Rinko and compassionate, klutzy, Adorkable Shunpei.
Kamen Rider Gaim initially features tough, assertive Mai who has no problem facing down a gang of bullies or challenging others to Invase battles; and soft-spoken Mitsuzane who dislikes confrontation and wears pink pants with his dance uniform before his Heel-Face Turn.
Nigel and Sydney of Relic Hunter were pretty much a straight inversion of classic adventure stereotypes. She was the action star, impulsive, fearless one and he was always in need of being rescued. Sort of uneven in that she also often got to be the smart one and the people person.
Jane and Brad on Happy Endings-not as pronounced as some examples, Jane is fairly feminine, she's just take charge and aggressively helpful (read: controlling), Brad meanwhile is Camp Straight, but is also a classic example of the male breadwinner. Also they both look exactly as masculine and feminine as normal, Brad is usually dressed in a suit and classicaly handsome, and Jane shows off her legs every chance she gets.
Friendship example: Fez and Donna. He and his girlfriend Big Rhonda subvert it, since she's bigger and stronger than he is but is also an awkward Huge Schoolgirl.
On Will and Grace gay Jack and straight boozehound Karen go to a meeting of an organization that promises to "cure" gayness. There they meet a married couple with a stereotypical effeminate man and very masculine woman who praise the organization. After they walk away, tipsy Karen asks "Was that two men or two women?"
Of course, Will and Grace in general subscribed to this so much that it might honestly be considered a Gender Flip of a traditional sitcom. Grace was a stereotypical sitcom man: a brash, lazy, slovenly, Big Eater who found gay porn to be exciting the same way a lot of men feel about lesbians. Will, who started Straight Gay but Flanderized into Camp Gay, was much more a traditional female sitcom character: much more calm and rational (initially,) who was the more uptight and decorated their entire apartment and did all the cooking and cleaning. In that sense, Jack and Karen could be Will and Grace Up to Eleven (he was obsessed with fashion and jewelry, she was a violent drunk.)
The X-Files was designed partly around this trope. Mulder is emotional and intuitive, cries a couple times a season, and tends to lose fistfights or drop his gun at important moments; Scully is logical, scientific, emotionally reserved, and has Improbable Aiming Skills.
When Rosie O'Donnell hosted SNL in 1994 she did a sketch called "The Tomboy & the Sissy" with her as the 'tomboy' and David Spade as the 'sissy.' They are high school outcasts who become friends and help the other become more masculine and feminine.
Exaggerated like hell in an episode of RuPaul's Drag Race, when the drag queens were tasked to give glamorous makeovers to a group of tomboyish female martial artists who have never worn makeup or high heels in their lives.
Castle has elements of this; we have tough-cops Beckett & Gates (who is even addressed as 'sir.') Castle, Ryan, and even Esposito have strong metrosexual tendencies (lampshaded in one episode when they were going on about a line of men's grooming products, and Beckett said that it was 'Like Sex in the City with boys.'
In Once Upon a Time in Wonderland Alice comes across as the very proactive, no-nonsense, sword-swinging Action Girl, whilst Cyrus is a lot more gentle and sweet. The drive of the narrative also revolves around Cyrus being a Distressed Dude and Alice being on a Quest to rescue him. Plus the flashback reveals that she was the one to first make a romantic move on him.
In Warehouse Thirteen, Myka is a no-nonsense Action Girl and Pete, while he's ex-military, is generally more open about his emotions, and has a minor superpower he calls "vibes" which if he were female would look a lot like "feminine intuition".
Rackham and Anne Bonny of Black Sails are both pirates. But he prefers to use his mind over his brawn and wears flamboyant clothes that got his historical counterpart his nickname of "Calico" Jack. Anne is sexually aggressive, possessive of him, and does the killing in the relationship.
The twins Apollo and Artemis might be considered such, but only by modern standards. Apollo is sometimes thought of as a bishounen and He is the god of, among other things, music and art. He also spends a lot of time with the Muses. To classical Greeks, however, he was all man. Artemis, meanwhile, is a wild Action Girl who spends most of her time hunting in the wilderness with her Amazon Brigade.
Athena and Ares. Both Gods of war and victory, but the male Ares is something of a Glass Cannon and a serious Miles Gloriosus while Athena kicks his ass every time they fight, and is a Genius Bruiser to boot.
Ares is the personification of "manly men" fighting though. He's pretty much Dumb Muscle, while Athena fights to win. One author puts it rather well: Ares is chest banging and glory-seeking, Athena is the goddess of Nuclear War.
"Exotic" Adrian Street and Miss Linda. Adrian was one of the most successful wrestlers to use the Gorgeous George gimmick, and Linda played a feminine inversion of the gimmick by being tough, aggressive and dressing in black leather. Successors include Rico Constantino and Miss Jackie, Paradise and CJ Lane
By the standards of the time, Romeo and Juliet, based on the notion that Romeo was emotional (a traditionally feminine trait) while Juliet was practical (a traditionally masculine trait). In fact, Romeo's Hot-Blooded nature puts both of them into HUGE trouble when he kills her cousin Tybalt to avenge the death of Mercutio, and Juliet is the one who, with the help of a local priest, tries to brew a plan to get both of them out of it.
This applies to some degree to many of the lead couples in Shakespeare's comedies; the woman is typically wittier and more practical, and the guy is emotional in different ways (Hot-Blooded, brooding, etc.)
This idea is played with in Macbeth, with Lady Macbeth being the more aggressive and ambitious of the two. In fact as soon as she finds out about the witches prophecy she immediately begins formulating how to kill Duncan. While Macbeth is torn with internal guilt about his feelings, she's the one that goads him into doing it by questioning his manhood and saying he has no courage. Of course, after the murder they "switch back" with Macbeth turning into a kill-crazy tyrant and Lady Macbeth so wracked with guilt that she goes insane.
Tends to show up with Alistair and a female player character; consider this (possible) exchange from the sequel:
Alistair: Well, I suppose I should get back to the old ball and chain.
Teagan: You know, [she] hates it when you call her that.
Alistair: No she doesn't. Just because she killed an Archdemon... she doesn't scare me.
Teagan: You keep telling yourself that, Your Majesty.
From the Witch Hunt DLC, we have Finn and Ariane. Finn is a rather foppish mage that despises the outdoors, while Ariane is an experienced Dalish hunter. Just listen to their dialogue 
Aveline and her husband Wesley in Dragon Age II, in the beginning. Her later Love Interest Donnic seems this way initially, but subverts it; though he's less ambitious and more impulsive than Aveline, he's as tough, competent, and eager to battle as her.
Seisen no Keifu has Brigid, an assertive sniper raised by pirates and sensitive, submissive horseback archer Midayle as a predestined pair; to a smaller degree she has these dynamics with her other predestined lover, the archer Jamke, who is similar to Midayle but more reserved. Another one would be Tiltyu, the TsundereBlack Magician Girl, and her shy childhood friend and local Badass Adorable Azel.
In Rekka no Ken, we have Lad-ette Vaida and gentle, honorable Heath. Kent and Farina are a borderline case; Kent isn't exactly feminine but he's somewhat shy and very reserved compared to the outgoing, tomboyish Farina. (Who says he, personality wise, reminds her... of her older sister Fiora.)
Radiant Dawn includes Rafiel, prince of the heron laguz, a race too emotionally and physically fragile to attack enemies. The woman who saved his life, to whom he is now wholly devoted? Nailah, the wolf Laguz Royal (read: absurdly badass Crutch Character). One of them wears an elaborate robe, sings like an angel, and has ankle-length golden tresses. Guess which?
Of the many possible pairings in Fire Emblem Awakening, there's Sully/Libra (foul-mouthed Lad-ette and feminine War Monk) from the first generation and Kjelle/Brady (strength-obsessed female knight and a priest who's very in touch with his feminine side) from the second. Hilariously, Kjelle is Sully's daughter... Like mother like daughter, huh?
A Female Shepard and either Thane or Kaidan can come across like this, especially if Shepard is a hardass renegade. Shepard has to be the strongest human in existence, can drink anyone under the table, headbutts krogan like it's nothing, and generally is a stoic character. Thane and Kaidan meanwhile are sensitive and fairly soft-spoken, very moral, and the former waxes philosophical every so often. As a bonus, at the beginning of Mass Effect 2, Shepard will be clad in black N7 armour, whilst Kaidan is in the pink and white Phoenix armour.
Paragon!Shepard and Jack tends to look like this; while Shepard may be no slouch in the Badass department, he's still a calm, polite, and rule-abiding guy stacked up against the generalinsanitythatisJack.
Kaidan and Ashley have something of this dynamic as well. The best illustration comes from the Citadel DLC, even though only one of them is alive at that point. Regardless of gender or romance, Ashley and Shepard have a drinking contest that turns into a bar fight while Kaidan and Shepard have a quiet evening in while Kaidan cooks, though they also drink heavily.
Meryl and Johnny in Metal Gear Solid 4. When he proposed to her, she declines. Because she wanted to do that and proposes to him half a minute later.
Meryl and her partner Dave in Policenauts also qualify.
Lucas and Kumatora in Mother 3. They're not exactly a couple, but they are in the same party for half the game. Lucas has been described many times as a crybaby, and even when he seems to man up a bit later on, he still comes across as sensitive (especially with Love being his favorite thing). Kumatora is the tomboy of the group, and even has Boyish Short Hair and hates wearing dresses. And then there's her tough attitude and willingness to fight.
Homer and Edy from Valkyria Chronicles qualify, with the former being a meek, pretty little masochist and the latter a Hot-BloodedIdiot Herowhocan't sing. Likewise Karl and Lynn. Although they have similar temperaments, Karl is an engineer supporting the troops while Lynn is in the front lines as a shock trooper.
Dangan Ronpa: Naegi and Kirigiri are a non-romantic (aside from a little Ship Tease) example. It's based on personality rather than appearance; Kirigiri is aloof, proactive and willing to take risks, while Naegi is friendly and understanding, but more passive. Kirigiri is also taller than Naegi (granted, he is the second shortest in his class, along with Asahina). And she saved his ass a bunch of times during the game. There's a reason fans consider Naegi the heroine and Kirigiri the true hero, after all.
In Fate/stay night, Saber has spent her entire life playing the role of king, has excellent swordsmanship skills, and is uncomfortable around her emotions, while Shirou has little combat ability but takes great pleasure in and excels at domestic tasks such as cooking. The fact that, despite this dynamic, Shirou still insists on taking up a Stay in the Kitchen attitude (at least at first) generates a lot of the What an Idiot sentiment among the fandom, which leads them to miss how Shirou's reasons behind that are... well, more complex.
Hatoful Boyfriend has best friends Hiyoko and Ryouta. Ryouta, the boy, is a gentle, very caring "vegetarian male" who loves cooking and frequently crossdresses in fetishistic maid or magical girl costumes for his various jobs. Hiyoko, the girl, is a tough, impulsive cavewoman who can't concentrate without red meat in her belly (mostly from animals she kills either bare handed or by smashing with weapons).
Little Busters! has Kurugaya and Riki. While Kurugaya is definitely feminine in appearance - very, very feminine - she's a very competent, intelligent, intimidating Action Girl who loves to dote on her cute classmates as a Cool Big Sis. Riki, being a rather short, feminine-looking, shy guy, is very much included in her 'cute classmate' category. This causes him a bit of angst in her route as he feels like he should be acting cooler for her, but Kurugaya genuinely enjoys taking care of him, and by the end he's happy with seeing her occasional cuter side.
In Digger, due to the matriarchal nature of hyenas, gender roles are reversed and this arrangement is the norm rather than the exception. One character, a scrawny skin painter, has to compete with every other male in the tribe for the affection of their strongest warrior.
Last Res0rt toys with this when it comes to Jigsaw and Slick — Jigsaw's a bit of a tomboy (her main team color is light blue), while Slick's not above dressing in harem wear (and his team's main color is purple). Of course, they're not quite an Official Couple.
Homestuck: Tavros and Vriska. Tavros is a sweet, shy, kind boy with low self-esteem and a great love of animals and fairies. Vriska is an aggressive, dominating Munchkin and a Jerk with a Heart of Gold with emphasis on the 'jerk'.
In Girls with Slingshots, Zach is jokingly called the "girl" of his relationship with Hazel, because he's more sedate, mature, and wants to settle down and start a family, while Hazel is a rowdy, irresponsible boozehound. Their differences ultimately prove irreconcilable.
Siblings Cucumber and Almond of Cucumber Quest: He's a sensitive mage and very much does not want to be a hero while she's an aggressive swords-woman and wants to be a hero so much that she hands over the magic orb that will bring the Big Bad into power because it sounded more fun than just keeping it hidden forever (it could also be shout-out to the kind of games the story is modeled after).
Zigzagged with Beta Couple Keith the Basitin and Natani the Keidran in TwoKinds. Natani is bigger Keith, snores loudly, dresses in the most masculine fashion possible, and outright refers to herself as male due to being a FtM transsexual. Keith, meanwhile, is far more emotionally sensitive than Natani, and manages to be even shyer than her when it comes to romantic matters. It's zigzagged because both characters display feminine and masculine traits — for example, Keith is emotional, but is also the superior fighter, while Natani has shown some feminine shyness and modesty in the past.
The author likes to tease this interpretation, though, since there's a number of pictures of Keith in feminine positions and clothing, up to and including a piece titled "The daily life of the Kaisers" that depicts Keith and Natani as a 1950s-ish couple: in it, Keith is wearing the housewife outfit and Natani is wearing the masculine suit.
Also done in Suburban Knights with Obscurus Lupa/Critic when she's out of character. She pulls Critic around by his tie, will teach him how to be ladylike whether he likes it or not and eventually pulls out a gun against the enemies while he's learned his "bending like a girl" lesson.
Rebecca Stoné and Tacoma Narrows in Demo Reel, as she's a Lady Drunkberserker who'll genuinely try to kill you if you hurt anyone she cares about, while he's the Only Sane Man who likes the fact that he looks good in a dress and finds it better to talk things over. She and Donnie also fit the dynamic.
Parodied in this (NSFW) YouTube video, where the girl dresses up increasingly like a guy.
Should we mention that they were created by the same guy, Gunpei Yokoi, and that some consider them to be siblingsnote In either a literal or spiritual sense?
Monster High Clawd and Clawdeen, this is well played as Clawd is more Sensitive guy then Manly man. Heck, he's even afraid of his own fierce-acting little sister!
It should be noted that this is only by comparison as while sensitive, Clawd is the captain of the Casketball (basketball) team and is largely seen as The Big Guy / Big Man on Campus alongside Deuce. Clawdeen in turn isn't as masculine as she is sharp witted and fiercely protective of her friends, as this comes up when he begins to start dating her best friend Draculaura. In the past and on usual terms neither are seen this way.
In RWBY, the famous athlete and warrior Pyrrha Nikos is partnered with Jaune Arc, a scrawny Cowardly Lion whose greatest assets are his strategic mind and talent with Aura. This is furthered by their dance subplot, in which Jaune is romantically demonstrative and Pyrrha- although she feels the same way- doesn't know how to express it. note This trope is lampshaded during the actual dance, in which Jaune ends up wearing a dress.
Alongside them are Nora, a bloodthirsty, socially assertive hammer-wielder, and Ren, an introverted kung-fu student who dyed his hair pink and makes excellent pancakes.
There was a subtle example in an episode of Animaniacs. Charlton Woodchuck's parents meet traditional gender stereotypes at first. His father appears to be a farmer, and his mother is crying because her son is leaving home. However, when Charlton returns home his parents are sat in rocking chairs by a fireside and, in a reverse of traditional gender stereotypes, his mother is reading the evening paper and his father is knitting using a pink ball of wool.
The episode where they watch a play based on the series lampshades this by having Aang portrayed by a Genki Girl woman and Toph by a huge Boisterous Bruiser bodybuilder man (and she actually liked the idea).
Speaking of which, Sokka and Suki. Granted, it's not as extreme, but these two are respectively sensitive and tomboyish enough to qualify, though to an understandably lesser degree.
In follow-up series The Legend of Korra, we have Avatar Korra herself (an Amazonian Beauty version of The Lad-ette whose first impulse to a fight is to bust heads until she's the only one standing and responds to a guy she's eating out with belching by starting and winning a Burping Contest) and Mako (much more thoughtful, controlled and level-headed), arguably. More closely fitting, in season two we have Eska (a domineering, fearless, take-charge girl) and Bolin (emotional, sensitive, kind of wimpy boy).
Kim Possible and her sidekick Ron; she's a relentless overachiever who knows "sixteen forms of kung fu," set herself up as an international Teen Superspy, and kicks supervillain butt. He rarely fails to back her up and has his badass moments but is an easygoing type widely thought of as a loser, content to chill. Slightly mixed up in that she still fulfils gender roles such as cheerleading, while he eventually becomes a football player, but then again we see their old Halloween costumes - Kim as a cowboy, Ron as a ballerina. Nuff said.
On the villainous side of the fence, tough-as-nails Shego and sensitive and sometimes downright pouty Dr. Drakken.
Superjail! has Alice as the masculine woman and the Warden as the feminine boy. One episode in season 3 "Specialneeds" has Alice having to rescue Warden (who is in a full-body cast) from inmates who wanted to kill him.
Archer has Lana and Cyril. Lana is a powerful secret agent who is a crack shot with all manners of guns and rifles and has a hot temper to match while Cyril is a meek introverted accountant who loves to cook.
Wander over Yonder has Wander and Sylvia. She's an Action Girl who unlike Wander, dislikes cutesy or lovey-dovey stuff and has had to rescue him on several occasions. Wander is a bit more of a Love Freak and has cross-dressed on a few occasions.
Groj Band has Carrie Beff and Larry Nepp. Despite having very little screentime, their body◊ language◊ portrays Carrie as the strong one and Larry as the softspoken one.
Polish pianist, composer and Ill Boy Frederic Chopin was paired up with George Sand (the nom de plume of Amantine Dupin), a Tom Boy writer overlapped with The Lad-ette.
Their enemies tended to portray Marc Antony and Cleopatra as this, to insult him and make the Romans fear her.
Japan now calls this the "Herbivore Man, Carnivorous Woman" phenomenon. In short, more men are identifying themselves as meek, passive, and indifferent to the opposite sex while women are becoming more assertive, aggressive and eager to date. Thus, it's not uncommon for women to walk up to man they're interested in and ask for his phone number, a date, or even sex. Whether this is a good or bad thing depends on whom you ask.