Epigraphs are like little appetizers to the great entrée of a story. They illuminate important aspects of the story, and they get us headed in the right direction.
"To My Father and Mother"
We get a heavy dose of Freud in The Hero with a Thousand Faces, with gods, goddesses and monsters all representing some kind of grappling with the gifts and anxieties we all get from our parents. Like it or not, Campbell seems to be saying, we all have some mommy and daddy issues.
The Hero's Journey in part is about how to navigate our relationship with our parents, and how we use the lessons they teach us to become our own people independent from them.
Campbell certainly isn't shy about it when he cites examples in the book:
The hearth in the home, the altar in the temple, is the hub of the wheel of the earth, the womb of the Universal Mother whose fire is the fire of life. (39.2)
and
And the testings of the hero, which were preliminary to his ultimate experience and deed, were symbolical of those crises of realization by means of which his consciousness came to be amplified and made capable of enduring the full possession of the mother-destroyer, his inevitable bride. With that he knows that he and the father are one: he is in the father's place. (111.2)
So the epigraph kind of has a double meaning. On the one hand, Campbell wants to give a shout-out to dear ol' Mom and Dad. But he also wants to acknowledge the symbolic importance of mothers and fathers, and the way they function within the context of the Hero's Journey.
It's a clever twist, but then again, Campbell is a clever guy; we probably should have expected it.