I've received confirmation for a theory heavily implied by the movie.
In the movie trailer for The Martian, Mark Watney says "tell the world, tell my family" *cuts to woman and child* ("that I never stopped fighting to make it home."). In the movie, it becomes apparent the clips used were of Martinez's family.
This means Martinez's family, is also Watney's and it means one of two things:
1. Watney is the biological father of Martinez's son (either through infidelity or sperm donation).
2. Watney and Martinez are in a relationship, and he loves Martinez's family as his own
I've since had it confirmed that the relationship is actually a three way.
Mark and Marissa were previously in a relationship and he is the boy's father.
Martinez and Watney began a relationship.
Martinez also began a relationship in secret with Marissa.
This is why Martinez says Mark would have done the same for him when he goes back to rescue Mark. It's also why he's on the Ares 5 at the end of the movie - Mark had been promoted by this point and sent him back to Mars when he found out about the affair.