Offsrping is a child produced by a male and a female.
Family is a combination of parents and children and can include extended relatives.
Okay, so if a marriage is withouth children/offspring, what then? If a single mom who never marries has and raises children, is that not still a family? See, these things are not always associated with "marriage".
Gay people can adopt children and they can call themselves a family. That meets the criteria of your marriage association, correct?