the question is already in the title. If possible, it might be extended to: Have animal taxa (mammal) who tend to live in a family structure have a monogamous sexuality? Or are there cases of these taxa, where the sexual partner is not the social one.
Regarding gibbons, yes. According to National Geographic:
Gibbons are monogamous and live in family groups consisting of an adult pair and their young offspring.
There isn't a generalized answer for "family living", although specific family types are indicative of relationship type. Nuclear families (parents and children) tend to be monogamous, families with multiple males and one female tend to be polyandrous, and families with one male and multiple females tend to be polygynous. See this page on primate social structure for more information.