There are very important clues in the story to take the story as an epic journey. The title uses the words Human Comedy, a play on Dante's Divine Comedy, and Homer and Ulysses are names with obvious references. Through the epic saga of everyday life, Homer, the protagonist, endures a journey to become an adult capable of functioning as a leader in his home, even with the painful knowledge of death and horror that comes from WWII and he deaths of his father and brother.
The quest from innocence to experience is hinted at throughout the play, especially in the relationship between Homer and his small town community. When he goes to work, he does his job, which is to communicate messages to families that their sons have died in war. That means that experience and death are always on his mind, but it isn't until the message comes for his brother that he is finally tested. He must now step up to the plate for his family, because he is the eldest male; both his father and his brother have died.
So how does he manage? There are three major helps to him: first, there is the town itself who works together to form tight community bonds so that people don't go unnoticed. Then, there is the visit from the spirit of his father (another important allusion to epic poetry), and there is the hope that comes from his thirst for life, primarily demonstrated as a crush. He has a crush on Helen (another important Greek name, especially since in real life, Homer wrote the Iliad about Helen of Troy), and through that desire, he sees the benefits of surviving. He decides to take solace in the fact that he is not alone; when Tobey comes home, they accept him as family, showing that the deaths are forcing the community to be a big family.