Third-Person Limited: Look Who's Talking
If we were to get super technical—which, you know, we do—then we would say that Interview with the Vampire is told in third-person perspective.
We can hear you now. "But Louis narrates the story!" you cry. And you're kind of right, except for the fact that we can't get inside his head. All of Louis's narration is done in dialogue form. This is an interview, and he is talking to someone, which is why about 99.8% of the paragraphs in the book are surrounded by quotation marks. Louis is talking to us. This is different from the kind of internal narration you get in standard first-person vampire novels like Twilight.
Louis's narration is about as first-person as a Jay Leno monologue. We don't know what he's thinking, only what he says he's thinking. Which makes us wonder: can Louis be trusted?