Personally, I'd class Bakemonogatari as a comedy more than anything else, although it is hard to put it in one specific genre. It's just a very specific type of humour, most of which is language based, so it tends to lose a lot in translation, and isn't funny for everyone to begin with. Just the way the characters talk, how their dialogue is arranged, things like that are, not laugh out loud funny exactly (and not intended to be), but amusing. And there are a lot of subtle puns, references, and other jokes in there too which do not translate well. So I'd say that it's a comedy even outside the obvious funny bits which everyone gets. But it is a very strange show.