Pride and Prejudice is a comedy that uses situational irony and Horatian satire to show the sexism and inequalities of social conventions (mainly marriage) during the late-Romantic and pre-Victorian era.
Most of the humor is Horatian satire, or parody. Austen is poking fun at the obvious flaws in this stuffy, overly-stratified society. Her satire is subtle, not Juvenalian like Swift's--she does not attack, and her targets are not personal ad hominem attacks.
Most of this satire in the novel is situational and verbal irony. The former is derived from Mrs. Bennet's matchmaking scenarios, and the latter comes from dialogue of Mr. Bennet, Elizabeth, and Darcy. As such, these two forms achieve high comedy, a thoughtful laughter which originates from her heroic eirons, those who are self-deprecators.
The other form of humor found in the novel is low comedy. This is physical comedy, mainly from Mrs. Bennet's hysteria. She swoons between nervous breakdowns and excitement over any rich suitor. It's also found in Mr. Collins' excessive bowing. As such, Austen uses low comedy when dealing with alazons, those who think they are better than they really are.