Action Hero: Averted. He tries to be all tough and macho, but everything just backfires on him. On the DVD Commentary, John Carpenter and Kurt Russell said that Jack is a man who thinks he's the action hero, but really he's the sidekick.
Bad Ass: Appears less so compared to Wang, but he is a legitimate badass too, willing to walk into mortal danger beside Wang, taking out quite a few Mooks over the course of the film, and of course killing Lo Pan.
Humanoid Abomination: Whatever Lo Pan is, he's no longer human. He can appear young or old. He may be a ghost "playing at being a man," he may be possessed by a demon, he may have only made a deal with (or been cursed by) a demon for immortality, but Lo Pan himself claims that he is "like nothing you can understand."