Twig's father is the alpha of the Deer-Fox Herd that Twig originally belonged to. He is notably larger than an average deerfox, and has bigger antlers than the other males in the herd. Twig's mother looks like the other female deerfoxes.
They are first seen in "Chapter 9: The Deerfox". A few years ago, they lost Twig when he ran off to rescue Hilda from an eagle while the rest of the herd returned to their home dimension. In the present, Twig reunites with them and, after saying goodbye to Hilda, returns to their home dimension with them. The two realize however Twig's heart is with Hilda, and allow him to go back to her.