Psychological Thriller
Surfacing is kind of hard to pinpoint genre-wise. It starts out with some elements of detective fiction—since the search for the narrator's missing father initially drives the action—but then it becomes much more about the psychological acrobatics and relationship twists and turns that the four main characters become involved in.
The search for the narrator's father quickly takes a backseat to the narrator's own pursuit of self-knowledge, as she digs deep into her past and confronts some truths she had tried to "sink" some time ago. Alongside all that, there's a lot going on in terms of the characters' relationships—for example, between the narrator and her boyfriend, Joe; between David and Anna; and between Joe and the narrator and David and Anna.
Like what, you ask? Well, Joe wants to marry the narrator, but she's not super-sure about that idea, so there's quite a bit of friction there. And then there are David and Anna, who initially appear like the perfect couple (to the narrator, at least), but they soon make the narrator (and us, right along with her) privy to a lot of drama and even abusiveness and nastiness in their relationship. Case in point: David spends half the novel hitting on the narrator in front of his wife, seemingly with the specific intention of bothering her. So, yeah, they don't really seem like the perfect couple—and that veneer just crumbles more and more as the novel goes on.
On account of the mind games and intense focus on psychological self-discovery, we'd say this novel fits the "Psychological Thriller" genre better than any other.