The humorous elements in the story would, I think, be uniformly regarded as dark humor, or perhaps sarcasm, knowing what we know of Montresor's intentions and true opinion of Fortunato.
The humor mostly comes from the occasional turn of phrase by Montresor, or an unfortunately comment by Fortunato, both of which are generally foreboding and making light of Fortunato's impending demise. For example, Montresor attempts to get Fortunato even more drunk while in the catacombs, to ensure his compliance with the plan. Montresor drinks to Fortunato's "long life", knowing perfectly well that it won't be very long at all. He also drops little comments like "you are a man to be missed" and the mention of his family motto, which translated means "no one insults me without punishment".
Perhaps the final point which can be considered humorous is the verbal exchange where Fortunato attempts to determine whether Montresor is a Freemason (a fraternal society commonly referred to as Masons), and Montresor responds by showing him a trowel, a comment tool of masonry, as if he takes Fortunato's term "mason" literally. This is, of course, another foreshadowing of what Montresor intends for him.