Families in the community are not the same as ours. They really don’t have generations in the same sense either. There are parents and children, but none of them are related. There is no such thing as grandparents.
In the community, adults who decide they are ready to raise children apply for a spouse. The Committee of Elders determines a suitable match based on compatibility and pairs them. They spend at least three years together before applying for a child. They are not romantically involved, and they are together only to raise the children.
Children are the product of artificial insemination of women known as Birth Mothers. Babies are raised together by Nurturers until the Ceremony of One in December, when they turn one and are given to a family that has applied for them. Families consist of one boy and one girl, and the parents decide when to apply for the second child but it is not common to wait more than a few years between the two.
After the youngest child grows up and moves out, the family unit disbands and the parents go to live with the other Childless Adults. They have no further relationship with their children or each other, and often no contact at all. When they get too old to work , they move into the House of the Old and live there for a few years until the community decides they have lived long enough and they are killed by lethal injection.
In the book "The Giver" by Lois Lowry certain people are given the job as being birth parents. It will be their job to have three children. Parents are trained and prepared before they are considered ready to become a parent. They are called the protective parental unit and are paired as a couple. However, sexual relationships do not occur. Until the children are ready to be placed in homes they are kept in a center where people called "nurturers" care for them. Jonas' father is a nurturer. Parents are matched with their children by the elders. The elders control all the decisions.
I do not believe that the family's are actually generational since the children have come from a different parental unit at birth. They are then nurtured in a separate setting before being given to parents to raise them.