Medieval Islamic Family
According to the Quran, Muslim men were allowed to have as many as four wives if they were rich enough to take care of them all, but most men in the Islamic world still had only one wife. In fact, most people in the Islamic empire lived as people had in the Roman Empire and the Sassanian Empire before them: in families with a dad and a mom and a bunch of kids, and sometimes the dad's mother and his unmarried brothers and sisters (the kids' aunts and uncles).
In those days, the government didn't allow men to marry men, or women to marry women, as they can today. But there were many non-traditional families anyway: households where the dad had left, or died, or where unmarried brothers or friends lived together. And not everyone lived in a family: Lalla Arifa, for example, left her family to live in a Sufi monastery for women. People could get divorced pretty easily, much easier than in Christian Europe.
As with earlier times, other people also lived in the house and counted as part of the family. These were mostly slaves or employees. People in the Islamic Empire, like the Sassanians and the Romans before them, still didn't make much of a distinction between their families and their businesses.