Northanger Abbey is primarily a light-hearted comedy with lots of scenes specifically designed for a laugh. While it isn't a slap-stick, laugh-a-minute, Northanger Abbey does have all the elements of classic comedy. It's a series of humorous mishaps and misunderstandings that get resolved in a happy (and rather amusingly convenient) ending. The other genres that represented are also infused with comedy. In fact, comedy serves as something of an umbrella genre here.
First, we get a comedic coming-of-age narrative. The entire narrative trajectory of works as Catherine's coming of age story. She starts out as a naive and inexperienced youth and ends up a lot wiser and more adult. Most of the major plot points and incidents, both comedic and more serious ones, are linked to this theme of growing up. This is a novel about the often humorous experience of being young and growing older, mentally and emotionally.
We also get a very comedic portrayal of the Gothic genre here. OK, so Northanger Abbey is primarily spoofing Gothic novels, but it does have some things in common with them, deliberately so. Gothic novels are all about the dread. Suspense, anxiety, looming disaster, and all that stuff are at the core of the Gothic genre, from Dracula to The Turn of the Screw. Northanger Abbey lacks supernatural and horror elements that generally make up the Gothic, but it does have lots of suspense and anxiety. Catherine spends a lot of the novel dreading things, whether they be the consequences of a major social mishap or the latest actions of a crazy General, who lives in a "Gothic" Abbey. Unlike the traditional Gothic genre, Northanger Abbey uses Gothic tropes, or elements, for humorous effect.
Romance is also depicted humorously here. Love and relationships abound in Northanger Abbey, which is largely about the relationship and eventual marriage of Henry and Catherine. We see a lot of other relationships and marriages depicted as well: Isabella and James, Isabella and Captain Tilney, John and Catherine, General Tilney and his dearly departed (and fortunately not murdered) wife, Mr. and Mrs. Allen, etc. Romance and love are complicated, messy, and above all very funny here.
Northanger Abbey also boasts of all the hallmarks of satire. The text mocks human folly in general as much as it mocks over-the-top Gothic novels specifically. From start to finish, the text is one giant parody of the standard Gothic novel. The text is also a bit of a mocking free-for-all too. Everything from friendship to romantic love to youth to courtship is ridiculed.