It is clear early on in The Giver that the Elders are in control of not just families but pretty much everything that happens in their society. Still, the level to which they control families is surprising, as people have no choice in forming their families. The Elders choose who will marry, and they assign spouses after a sometimes very long waiting period. That's not to say that spouse assignment wasn't well-thought out; it just wasn't considered by those who would actually be marrying.
Even the Matching of Spouses was given such weighty consideration that sometimes an adult who applied to receive a spouse waited months or even years before a Match was approved of and announced. All of the factors—disposition, energy level, intelligence, and interests—had to correspond and to interact perfectly.
Families did not have and then raise their own children; Birthmothers had the children, and the children were then assigned to families. The role of a Birthmother was not considered to be a respectable job, and once a Birthmother was done having children, they were sent to be Laborers. If a baby, called a newchild, did not thrive, they were released, which meant they were killed. Jonas' father is able to save a newchild from death by receiving a special allowance to attempt to save him.
Father had gone before the committee with a plea on behalf of Gabriel, who had not yet gained the weight appropriate to his days of life nor begun to sleep soundly enough at night to be placed with his family unit. Normally such a newchild would be labeled Inadequate and released from the community.
Once children grew up and became adults and received their own assignments, families were no longer necessary, and they were disbanded. Jonas asks The Giver if he has a spouse, and The Giver laughs a little.
You're forgetting how old I am, Jonas. My former spouse lives now with the Childless Adults.
Jonas remembers that once he and Lily are gone, his parents will also go to live with the Childless Adults.