First Person (Codi and Hallie), and Third-Person (Doc)
Animal Dreams switches betweentwo narrators, Homer "Doc" Noline, and Cosima "Codi" Noline—although you could make the case that Hallie's letters up the number of narrators to three. Codi is the main character. It's her journey we're on, and her voice tells most of the story in first person; both Doc's chapters and Hallie's letters are short.
Hallie's letters are shown to us through the lens of Codi's perspective at some times, but at other times, they stand on their own in first person, too. Doc's chapters, on the other hand, are shown in an intimate third-person. The pronouns are "he" and "his," but the narrator also seems to be entirely in Doc's head, seeing what he sees and thinking what he thinks in real time.
Why does Kingsolver even include Doc and Hallie in the narrative if it's all about Codi? Because Animal Dreams is fundamentally a novel about memory. Doc has Alzheimer's, and the wild shifts between past and present in his sections allow us to see parts of Codi and Hallie's childhood that Codi doesn't even remember, or never knew about in the first place.
Importantly, the technique also lets us know how wrong Codi is about certain aspects of her upbringing. For example, she thinks Doc has never really loved her, but we know from Chapter One on that he always has, even if he chooses to show that love by never ever touching his daughters unless he's measuring their feet for orthopedic shoes.
Both Doc's letters and Hallie's give us some distance from Codi's relentlessly negative ideas about herself, and they help us see Codi for the unreliable narrator she is. In addition, the distance between Doc's and Codi's perspectives sets up one of the important conflicts of the novel: only when Codi learns to own her own past will she feel at home, either in Grace or in her own head.