Claude "Torch" Weaver, one of the Carnival of Killers in Black Lagoon is a religious man who won't touch alcohol and is the only person in the cast who never swears. He's also a completely insane pyromaniac.
The Joker, believe it or not. During the No Man's Land story arc, he kidnapped all of Gotham's newborn babies to further drive the city to despair, but did not harm any of them. (He did shoot Commissioner Gordon's wife when she tracked them down.). Grant Morrison's Arkham Asylum suggests that the Joker is just as likely to dote on children as he is to jab pencils in their eyes — it all depends on what you expect will happen. (He'll do the opposite.) In Legends of the Dark Knight: Duty, surveillance footage from a fair shows the killer clown blending in by handing out balloons and performing tricks for children.
Averted in bothversions of Batman: The Dark Knight Returns where he hands out poison cotton candy to boy scouts. The former shows the aftermath; the latter doesn't.
In contrast to his mostly depraved and foul-mouthed supervillain colleagues, the Doll-Master in Wanted is very much a Family Values Villain. He's always polite and well-spoken and never swears, and to his family, maintains the image of a normal and wholesome suburban father. Granted, his wife interprets his absences for villainous activities as signs of adultery, and he actually did cheat on her in an expedition to another dimension, but his wholesome persona is genuine. Shame that he's a ruthless criminal who kills without remorse.
Ma Dalton from Lucky Luke is an Anti-Villain example. She is a kind, proper, polite old lady, who doesn't hold with her grown sons swearing, who ensures they wash their hands and say grace before every meal, who doesn't want them consorting with women... and she has no problem whatsoever with the family trade of armed robbery (except when her sons do it haphazardly).
Light: He was supposed to call me back! I wanted to gloat some more before my flash mob tore him apart! A child I have never met before LIED to me! His parents should've taught him better... Oh! Oh, orphan. Right.
A popular trope in gangster movies like The Godfather and Goodfellas. The people involved are murderous assholes of the highest order, but they have a code, and nothing is more important than family.
Don Corleone: A man who doesn't spend time with his family can never be a real man.
Don Rafael Montero in The Mask of Zorro won't allow children to witness Public Executions he's staged to bring out Zorro, or tell his twenty-year old Spoiled Sweet daughter Elena that he put her real father in a dungeon to die and that one of his soldiers accidentally killed her mother (Montero also promptly shot that soldier for it).
Inside Man: The bank robber. Despite brutally beating a hostage, executing another one, and robbing the bank, he is concerned about the violent content in a video game a young hostage is playing, and resolves to discuss it with the boy's mother. Subverted in that the execution of the hostage was staged, and the only thing he actually stole was the contents of the safe deposit box of the bank's founder, which were ill-gotten gains from his days as a Nazi collaborator. The "villain" is a lot less villainous than he appears.
The warden from The Shawshank Redemption is ok with brutality, murder, corruption, and extortion, but don't try taking the Lord's name in vain in his presence.
Warden Norton: I believe in two things: discipline, and the Bible. Here, you'll receive both. Put you trust in the Lord; your ass belongs to me. Welcome to Shawshank.
In Under the Dome Second Selectman Big Jim Rennie is a born-again Christian who has refused to swear or drink since his conversion, and believes highly in family unity. That doesn't stop him from plotting a hostile takeover of the town, filling the police force with rape-happy Mooks, setting up the largest meth lab in the country, and killing members of his family. It's for "the good of the town," after all.
Villain Mayor Richard Wilkins III is really the pinnacle of this trope. He's made deals with dozens of different demons, founded a town specifically so he could lure in people to be killed by monsters, orders numerous thefts and assassinations (including against newborn infants), and his master plan is to become a giant demon that will devour everyone in sight. But he still believes in setting a good example for the children, is disgusted by "immoral liaisons" at the local motel, and his last words to his vampire army before the final battle are, "And boys? Let's watch the swearing."
René Benoit in NCIS is an international arms dealer who considers himself a businessman.
Gustavo "Gus" Fring in Breaking Bad is this to a T. Since nobody save for a select few even knows that he's the biggest meth kingpin in the Southwest, it allows him to put on a perfect Villain with Good Publicity act.
The Addams Family aren't really villains (though they do enjoy torturing, and allude to lots of rather nasty things) they are just dark and WEIRD (and kooky and spooky...), but they are very big on family values in almost all media in which they have appeared (values like family, friends, love, mayhem, manslaughter...)
In the Japanese series Kamen Rider Double, this was the Nazca Dopant's redeeming quality. He was perfectly willing to sell self-destructive and addicting superpowers to greedy and corrupt adults, but was horrified to find them being given to children as test subjects! Despite being The Dragon at the time, he teams up with Double to save the children. However, Redemption Equals Death his own wife, who remains evil throughout the whole series, kills him.
While there is some serious variability in how good they are at it, most of the mobsters in The Sopranos at least attempt to do this.
In The Straits, Harry is fine with drug-dealing and creative murder, but draws the line at arranged marriage for his daughter, and dealing in sex-slaves.
In the first season of Leverage, a gang boss is very angry when he learns one of his men took a job beating up a priest. He gets the guy to give the heroes the information they want before saying this man's path to atonement is about to begin.
Omar Little from The Wire isn't really a villain, but despite the fact that he's a violent criminal, he can't abide swearing.
All of Baltimore's gangsters can be taken into consideration since they all abide to the "Sunday Truce" in which all beef is put aside so the people of west Baltimore (gangsters and citizens alike) can attend church with no fear of violence. When the truce is violated, the two shooters are chewed out and ridiculed mercilessly for such a shame.
Azazel from Supernatural. In season one, two particularly evil demons turned out to be his children. He was not happy that Sam and Dean killed one of them.
The Alpha vampire has shades of this as well. He views all vampires as his children and even his Stockholm'd snacks call him "daddy".
The Governor from The Walking Dead is this. He hides his villainy behind a facade of Southern charm, and seems at time to genuinely care about the people living in the town. He is, however, not averse to committing acts of violence.
Livia Soprano (of The Sopranos) seems at first to merely be a grumpy old lady. She is very insistent that nobody swear or smoke in her presence. Then she all but encourages her brother-in-law to put a hit out on her own son.
When they're not on the job, many of the mercenaries of Team Fortress 2 try to be this, handing out human molars and inordinate amounts of blood money to trick or treaters, defending Snissmas shoppers from inhuman monsters, escorting unarmed noncombatants through deadly robot hordes, and helping children to conquer their fears through teaching them to commit murder. Moral Dissonance is invoked, lampshaded, and played for laughs, especially in the case of the Pyro.
General Tarquin of The Order of the Stick. He puts a "Baby on Board" sign on his war chariot, offers heartfelt apologizes to his partner in crime Malack when Tarquin upsets him, is unfailing polite, and a devoted father. But he also leads a militaristic nation, burns escaped slaves alive. In a comic that sums up his relationship perfectly, he is laughing heartily eating ice cream with his son, while walking past a statue of Tarquin beheading someone.
An equally good Tarquin moment happens before he's even introduced. When Nale describes the tyrannical general father who raised him, there's a panel depicting the then-nameless general slaughtering his enemies from a spiky war chariot... with a "Baby On Board" bumper sticker.
Malack himself easily qualifies. Just watch him discuss parenthood with Vaarsuvius, pursue vengeance against Nale for the death of his children, and forcibly turn Durkon into a new member of his vampiric "family" when their moral differences prove insurmountable.
Vaarsuvius: Have you considered adoption? I'm certain this war climate provides no shortage of orphans.
Malack: It has crossed my mind, but I'm worried about not having, you know, that special bond...
Black Manta from Young Justice deserves a place here for using a terrorist mission to teach his son a lesson about honesty.
Father from Codename: Kids Next DoorIS this trope. He hates the Kids Next Door and will do everything in his power to wipe them out, sometimes through some rather family-unfriendly horrifying means. However, since he is a father, he dotes on his own kids, the Delightful Children From Down The Lane, and tells them to mind their manners while they carry out acts of villainy, and behave in the presence of adults while they carry out acts of villainy.
A later example both plays this straight and role-inverts it; in one episodenote The one where the KND is trying to save someone from getting a bad haircut from his dad; long story, it's revealed that Mr. Boss and Numbuh 86 are father and daughter. They make it clear that the fact that their respective organizations are perpetually at each other's throats doesn't stop them from loving one another as family.
Mob boss "Diamond Jim" Colosimo had no problems running prostitution rings and illegal gambling in Chicago, but when Prohibition went into effect he refused to have anything to do with bootlegging (within five months Colosimo was shot to death and his second-in-command Johnny Torrio had moved into alcohol smuggling, but that would be another trope.)
A lot of mob bosses are like this. Little Italy in New York used to be one of the safest neighborhoods in the city, because people knew what would happen to anyone dumb enough to knock down a little old lady and steal her purse. Joseph Profaci, the namesake of the Profaci crime family, once allegedly had a man strangled to death with a rosary for stealing a chalice from Profaci's church.
La Familia Michoacana could be the best Real Life example. One of the most brutal drug cartels, obsessed with control of the Mexican state of Michoacán, fond of beheadings, and headed by "El Más Loco" ("The Craziest One" or "The Maddest One"), they forbid their members from doing drugs themselves and heavily promote (their atypical version of) Christianity. El Más Loco is also a fan of John Eldredge from Focus on the Family.
Mob hitman Richard "Iceman" Kuklinski, who claimed to have committed more than 250 murders over the course of his criminal career, hated working on holidays such as Christmas and Thanksgiving because he felt it was important to spend them with his family.
Then again, he would occasionally beat his wife and scared the ever-loving piss out of his children, so this trope was "played with" to say the least.
Actor Neal McDonough is an interesting partial example. He has absolutely no problem playing psychopaths and violent murderers and villains of all stripes and leaving teethmarks all over the scenery - but he's lost more than one job out of a refusal to do sex scenes (the logic appears to be that that he's an actor and not causing any actual physical harm to his co-stars with a villain role - but getting in bed naked with an actress is still getting in bed naked with a woman who is not his wife, even if it's in front of a camera.)
Joseph Goebbels was Adolf Hitler's chief propagandist and spin-doctor; as well one of his most devoted followers and, briefly, his successor. He was also well known as a devout family man and husband* By the standards of Nazi Germany, anyway. He cheated on his wife, but (probably) only once and expressed genuine regret, unlike most of the other party members, as well as a model father to his children, including Harald, his wife's son from a previous marriage.
The other wiki claims that Goebbels was cheating on his wife a lot, though. According to his own diaries.