Perry Cox and Jordan Sullivan have an unconventional relationship. They were married and later got divorced. They started seeing each other again and even had a son Jack, but have refused to get married again. They even found out that they were technically legally married, but decided to get divorced. They then had another child, Jennifer Dylan Cox (per J.D's recommendation).
Little is known about the remaining family, but Jordan's father was mentioned to be named Quinn. In the episode where Jack gets his name, Jordan considers naming Jack after her father, so their relationship was probably healthy. In another episode, Perry claims Jordan is basically the same as her mother, so their relationship might not be as good as Jordan-Quinn's.
In My New God, Cox mentions that his father used to drunkenly beat him and his sister, Paige, while their mother silently watched, resulting in Paige turning to Christianity.
List of family members