The Interpretation of Dreams is a scholarly, scientific text, so it's a little strange to think of Freud as its "narrator." But if we remember that Freud thought of his argument as a kind of hike or "walking tour" through new and exciting territory, then thinking of him as our narrator—or even as our walking companion or guide—makes a lot of sense.
Throughout The Interpretation of Dreams, Freud's voice is ever-present. He outlines the critical territory for us, he tells us lots of personal stories and dreams, and he even retells his patients' stories and dreams. Freud may not be telling us a "story," exactly, but he's certainly showing us the way.