Can you think of any other stories, books, or movies that blend horror and humor in a similar way as "The Cask of Amontillado"?
I think there is a certain amount of black humor in this story. The same can be said of "The Tell-tale Heart" and even "Masque of the Red Death." Sometimes death can be funny, if it is narrated a certain way. There is a creepy humor to it, I agree.
One of my absolute favorite movies is The Silence of the Lambs. This movie stars Anthony Hopkins as the evil, but oh so funny, Hannibal Lector. Con Air also stars a diabolical serial killer with a sense of humor. Years ago, there was a Wes Craven movie called Shocker, and it seems to that the killer in that movie was humorous as well.
Poe's "The Black Cat" has a moment of perverse ironic humor in it, too. When the narrator is tripped by the cat, he is enraged, "exasperated ...to madness." He raises an axe to the cat, but his wife "stayed" his hand, so he kills her simply because she is in the way.
Goaded, by the interference, into a rage more than demoniacal, I withdrew my arm from her grasp and buried the axe in her brain. She fell dead upon the spot, without a groan.
Regarding a film that mixes horror with comedy, Throw Momma from the Train starring Danny DeVito comes to mind.
If you're referring to the irony as humor, as suggested above, I might go with two choices: Roald Dahl's "The Landlady" and "Oedipus Rex" by Sophocles. Both of these stories has kind of a clueless character to whom something ironic and dramatic happens.
Well, your question presupposes that this story is actually funny, which some would disagree with. I personally don't see any of the humour that you obviously feel is such an evident part of the story. However, I suppose you are focussing on the irony of the text, such as when Fortunato asks what the motto is of Montresor's family, and, with dramatic irony, we see its grim significance, although Fortunato is blind to it.
So, if you want to find some parallels, I would suggest movies such as the Scream films, and maybe Kill Bill. Both contain moments of horror and terror and of course grim violence, but also manage to blend in humour by focussing on parodies of horror movies or spaghetti films and making fun of them whilst simultaneously shocking us.
Many of Poe's stories have similar plots and characters. As the creator of the mystery story and delighted in horrifying many readers. Similar horror stories might be Honoré de Balzac's "Le Grande Bretêche." Possibly I might add James Cooper's "The Last of the Mohicans."