It can mean either, and if someone said that to me, I would either have to use additional context clues or simply ask the person whether their family had stayed with them. Usually the expression would be followed by some clause indicating time, though obviously it doesn't have to be for it to be grammatical.
We had family over for dinner.
We had family over for the night.
We had family over for a couple days.
Bueno, "have the family over for dinner" quiere decir que la família vino a cenar. "have them over for the weekend" obviamente quiere decir que vinieron a pasar el fin de semana. Como siempre, todo depende del contexto. Saludos