Families in the Middle Ages were both like and unlike modern American families. But what, exactly, are modern American families like? It's actually hard to tell.
The stereotype is Mom, Dad, Sis, and Junior, all living together, but this is in fact a small minority of households these days--there are the childless couples, the people living by themselves, the people living with three generations, the step-parents, the people living with people they aren't related to or married to, and so on. Many of these groupings consider themselves family.
The "household" is a (more or less) recognizable unit, and the medieval Latin term familia meant household. Thus a medieval familia could include several generations of related people, servants, permanent house guests, and so much more.
In practice the basic medieval economic and social unit was the nuclear family, Mom, Dad, Sis, and Junior as we would consider it. This was true both of peasants and lords. Others might live in their households, but this grouping was the center. With a higher level of mortality than in the modern West, many of the adults would have been widowed and remarried, but probably not a greater proportion than those in modern times who have divorced and remarried.
Superimposed on this readily recognizable unit, however, was another definition of family, consisting of people who all descended from a common ancestor. Medieval people were much more conscious of their ancestors than are modern Americans, where most would have trouble coming up with the names of their great-grandparents, or maybe even grandparents. For aristocrats, ancestry was important because nobility depended on noble blood, being descended from nobles of whom one was very proud. Peasants too knew their ancestors, because most of them lived on land that had been in the family for generations and had heard ancestral stories all their lives.
But knowing that one was related to someone else did not mean that family feelings always predominated. Two brothers or two cousins who both had their eye on the same inheritance could end up seeing the other as the enemy.
And exactly who was and was not "family" varied with each individual. For a husband, his wife was not entirely an insider, belonging as she also did to her natal family. To her children, however, Mom was a central part of their "family." Aristocrats making gifts to a monastery might ask for prayers for relatives to whom they would never have left any inheritance.
Within a nuclear family, the oldest son had at least some precedence, but it was not automatic, and younger sons and daughters were considered full family members, with at least some right to their parents' property, and certainly a claim on any prayers their parents might win.
As modern Americans sit around the holiday table with a mixed collection of in-laws, siblings, parents and grandparents, children and cousins, aunts and uncles, and probably a few assorted friends and neighbors, everyone still calls it a "family" dinner. Family was just as flexible in the Middle Ages.