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.
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).
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!
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).
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.
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.
Amusing Injuries: Much less prone to it than Henry (and even so, the frequency varies by the season), but she does get her fair share of cartoon violence thrown her way.
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.
Genius Ditz: In season one. While she was pretty good with technology, in fact making her own inventions sometimes, she was as dumb as a box of rocks.
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.
Only Sane Woman: Certainly not in the early episodes, but she slowly starts to grow into this role as the show goes on - especially as the shows begins to emphasize Henry's arrogant Butt Monkey status. By the third and fourth seasons, Henry and June were trading off on this role, and often both played Only Sane Man to another character who was even sillier than they were.
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.
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.
Cloud Cuckoo Lander: 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.
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.
Sniz and Fondue
Sniz is a crazy little ferret/cat/thing who loves comic books and motorcycles. Often getting into trouble, his older brother (or roommate) Fondue will try calming him down.
Catch Phrase: "Snap me down!" and "Cut me an oversized wedge."