Protagonist
Character Role Analysis
Tilly
We see pretty much the whole story through Tilly's eyes, and on the whole, it's Tilly's story—that's how we know she's the main character, aka the protagonist. Even though Tilly's lens is usually turned outward on the other characters rather than inward on herself, Tilly is the connection between the frame story and the main narrative and between all of the other characters. So, Tilly's definitely our girl, through and through.
Delphine
There's an argument to be made for Delphine as the main character because she's the character Tilly seems most concerned with, and the character she has the most to say about. Delphine is really good at stealing the show, and she turns out to be the real reason Howard's father brings his sons to Illinois—she's his mother and Howard's grandmother. We could argue that the whole reason Tilly tells Howard the story is to give him the chance he never had to know Delphine. Instead, we'll let you argue among yourselves, though. It's more fun.