Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
Third Person (Limited Omniscient)
Fairy tales are big on third-person narrators—that is, a speaker who's not a character in the story itself. Briar Rose isn't a fairy tale, but it is a novel about fairy tales, so it makes sense that it follows that convention. Eh? You see what the author did there?
Two more things worth noting. The first is that most of the story zooms in on Becca, so it's her thoughts and feelings we're hearing about most of the time. (If the narrator were omniscient, he or she would have dirt on all the characters, Gossip Girl style, rather than just Becca. Then we would have found out, for instance, that Stan likes Becca back way sooner than we did.)
The second thing is that, for the portion of the book that focuses on Josef's story during the war, the third-person point of view shifts to follow him. It sounds weird, but it works.