Henry started the show as the more "normal" and laid-back host, especially compared to the (at the time) zany June. Eventually, while he was still calmer than June, he became the butt of almost every joke.
Adorkable: He's a bit awkward sometimes and is very cute.
Adorably Precocious Child: Moreso in the older episodes. Personality-wise, meaning. Appearence-wise? Got cuter.
Amusing Injuries: And unfortunately for him, he's at the butt of most, if not all, of them.
Balloon Belly: In the episode Sasquatch-ersise, along with June.
Berserk Button: Usually he's pretty agreeable. Call him a loser or relentlessly tease him, however...(June found this out the hard way when he got fed up with her mocking him and quit in the episode Won't Stick To Most Dental Work).
Hey, It's That Voice!: Noah Segan, who did Henry, was also in the 1995 season finale of Married... with Children as a kid blackmailing Kelly into going with him to his elementary school prom
Made funnier while he and Kelly were arguing, and it sounded like on of his many arguments with June.
Jerk with a Heart of Gold: He can be pretty self-occupied at times, even forgetting June's birthday (and making dickish comments after giving her a mood ring). But while he may not show it all the time, he deeply cares about her.
Love Hurts: In A Nut In Every Bite, he found himself falling for Mr. Stockdale's visiting granddaughter, Dawn. Unfortunately, he only seemed to be able to charm her by hurting himself. After Dawn leaves:
June: I'm sorry she had to leave, Henbud. Henry: I'm not. She was killing me!
It's not only with Dawn, but June, who has a crush on him, spends most of her time making his life Hell.
Minor Insult Meltdown: In Won't Stick To Most Dental Work, he storms off the show after June picks on him too many times.
No Respect Guy: Although he does occasionally get respect from June (she does have a crush on him).
Straight Man: In Season 1, to the ditzy and overly-excited early June.
The Power of Rock: In Your Logo Here, they attempt to make the show more educational by bringing in a singing otter who's more than a little like Barney. His teachings drive the kids crazy, so Henry lures him into a trap by playing a kickass electric guitar solo.
Yank the Dog's Chain: Happens to him a lot. In Won't Stick to Most Dental Work, he quits the show and opens his own restaurant. Despite it being very successful, he quits and returns to the show after seeing how heartbroken June was. And he's famous for falling in love, only to be rejected. But he finally gets his happy ending to that in the supposed "final episode", when June gives him a kiss.
While Henry was the calmer and more laid-back host in the early episodes, June was ditzy and just a little crazy. From Season 2 onwards, however, she became a lovable, good-hearted Deadpan Snarker. The only things that stayed the same were her cute looks and fiery temper.
Art Evolution: Obviously she changed as much as Henry, but inverted a bit. Her ponytail started out more "bushy" until season three-ish, where it became more of it's well-known teardrop-shape.
Break the Cutie: In Won't Stick To Most Dental Work, after Henry gets fed up with her teasing him and quits. She starts out reasonably well (if you can call angrily tearing up his letter and stomping on it "reasonably well"), but by the end of the episode, she's in tears because she misses him so much.
Breast Expansion: In a season two episode. And she was rather happy about it.
Depending on the Writer: Normally, she's a snarky yet good-hearted prankster with an attitude problem - however, in some episodes she's portrayed as a bossy brat. This stopped near the end of the show.
Even the Girls Want Her: One Season 4 episode reveals that she has some female fans who are so obsessed with her that they have based their entire appearance off her. And yes, they're as hot-tempered as she is.
Hotter and Sexier: She tried to make the show this in the episode Won't Stick to Most Dental Work. It was kind of out of character for her, but hey, Fanservice.
Pet the Dog/ Jerk with a Heart of Gold: She's bossy, snarky, agressive, bratty, and has a wicked short temper, but she has the biggest heart on the whole show, and has a very soft spot for animals. And despite Henry being the butt of many of her jokes, it's more than implied that she has a crush on him.
Kawaiiko: She made it into the show because the staff found her adorable. However, the trope is very much subverted.
Kubrick Stare: In the episode Hurts So Good, which revolves around a "Staplethon", in which viewers call in and donate staples. They aren't getting any callers at first, so June makes this face◊ and says "Did we mention that Bigfoot knows where you live, and he can pluck your head off like a grape?" The phones suddenly start ringing off the hooks.
The Lad-ette: As close as a 10-year-old girl can get.
Magic Skirt: The episode Won't Stick To Most Dental Work has her swinging on girders while singing a song...and wearing a dress, which clings perfectly to her the whole time.
Rapunzel Hair: The episode "I Just Don't Get it!" showed the duo's audition tapes. In June's, her hair was compltetly down, and it reached her knees. She most likely got a haircut before episode one.
Scout Out: The episode The KaBlair! Witch Project reveals that she used to be a "Logfire Girl", but was given the boot for her horrible cooking.
She Cleans Up Nicely: She's shown to be quite beautiful in a dress (as beautiful as the crude art style can get, of course).
Short Tank: She will wear a dress for more formal occasions, but it's stated in one episode that she dislikes wearing them and only does when she's made to. Which means that her little act in Won't Stick to Most Dental Work was most likely fanservice.
The Smurfette Principle: She's the only female character who appears in every episode of Henry and June, which is otherwise populated entirely by males.
You could change the show's name to "June and her Friends" and probably no one would notice.
Tertiary Sexual Characteristics: During her "cute" act, she shows her eyelashes. Usually, she doesn't have them (although early sketches gave her eyelashes)
Tomboy: To the point that a lot of people were shocked to discover that she's a girl.
Tsundere: Type B: She's usually sweet, enjoyable to be around, and laid-back. However, when something bad happens (like Henry giving her crap or something won't go her way), take cover.
Villain Protagonist: She's bossy, snarky, agressive, bratty, and has a wicked short temper.
Victoria's Secret Compartment: Slightly averted, as in the "Kablammy Awards" episode, June pulls the envelope (it says who won) out of the top part of her dress. However, since she's ten (and flat, unlike some ten-year-olds), it didn't get anything past the radar (unlike SOME stuff).
The Voiceless: Except for one moment in mid-season one.
Wouldn't Hit a Girl: As stated above, he never hurts June - Henry, however, is fair game.
Mr. Fred Stockdale
Mr. Stockdale is KaBlam!'s elderly network executive, and Dawn's grandfather. While he doesn't make many appearances, each one shows him to be senile, dim, and a bit corrupt.
Cloudcuckoolander: He's a Take That at executives everywhere: he's got the coherence of a five year old, more senile craziness than Mayor Adam West, and often has absolutely no idea what the show he controls actually is.
Executive Meddling: His major schtick is a parody of this - he often adds hilariously terrible (for Henry and June, anyway) new elements to the show for no good reason at all.
Shell-Shocked Veteran: In the episode The KaBlair! Witch Project, it's mentioned that he's served in an unspecified war... and several of his actions in the episode show that he still hasn't gotten over it.
Dawn
A one-shot character from the episode "A Nut In Every Bite". Dawn is the granddaughter of Mr. Stockdale, who comes from Switzerland to visit the show. Henry falls for her almost immediately (much to June's dismay), but she doesn't quite share the love. However, he does manage to charm her... by hurting himself. At the end of the episode, Dawn goes back to Switzerland, but by this point Henry is actually relieved (he's hurt himself so much he's covered in casts and bandages, and bound to a wheelchair).
Informed Attractiveness: Henry's "You can't just talk to a cute girl!" line to June seems to imply that he doesn't consider June cute... yet aside from the hair and outfit, Dawn doesn't really look that much different than June. Maybe Henry just prefers blondes.
Shallow Love Interest: Henry discovers that she's got a rather boring personality (especially compared to June) and doesn't return his affections, aside from finding him getting hurt funny. At the end of the episode, he realizes that she wasn't worth it and promptly forgets about her.
Sniz is a crazy little ferret/cat/thing who loves comic books and motercycles. Often getting into trouble, his older brother (or roomate) Fondue will try calming him down.
Adorkable: He's a huge comic book collector...and he's also a cute little animal.
Production Posse: Rick Gomez plays him, and also was in another show from the creators, The Adventures of Pete & Pete, as bully "Endless" Mike Helstrom. However, Will McRobb and Chris Viscardi (the creators) didn't know that he was going to be on the show (all the shorts had their own casting), and Gomez didn't know that McRobb and Viscardi were working on the show.
Continuity Nod: In the Sniz and Fondue pilot "Psyched For Snuppa", Fondue was called Squeaky. The show proper keeps the name as Fondue's rarely-used first name.