Here are some interesting questions. Is the family the foundation of society? Or is the society the foundation of the family? Which comes first, the family or society? Which is more important, the family or society? Should the family always include a mother, father, and one or more children to be called a family? Can there be families that do not meet these criteria? What policies should a society or government implement to maintain and strengthen its families? 
There are many different points of view on these topics. Views of families have changed over time in western countries. More families in western societies no longer have a two parent structure. Families now often have a combination of step parents and children, half brothels and sisters, or consist of unrelated members in, one family unit. Because of long distances for families in the U.S., many grandparents see their children/grandchildren only a little each year. In the Victorian period, in divorces, the children were usually put under the care of the father. Now, it is more likely that courts in the US will award the care of the children to the mother, or more recently, may allow the parents to divide the parental time of caring for the children by months, or even weeks. Approximately one half of all recent marriages in the US have ended in divorce, and society has had to adjust to this phenomenon as well as to make new laws and guidelines relating to former families that may now be separated by law.
During the Cultural Revolution in China, the attitudes toward the family would seem to have been very different than they are at present. Families were sometimes divided by ideology and children were often encouraged to report on negative activities of the parents to local leaders. Families were also encouraged to have more children to bring the nation to future greatness. Having a one child policy in the cities at present and two in the rural areas means that society does have an important influence on the family structure. In the cities, it creates an only child syndrome, which sometimes has negative influence on family structure.
Currently, it would appear that many Americans and Chinese would accept the idea that their family is very important in society, but is also regulated by societal laws, rules, and customs. There appears to be an influence going both ways. That is, the family structure affects society, and the society affects the family and its structure. It seems to me that all societies should make wise and generous policies to maintain and strengthen their families.
Here is my personal situation. I have had three children, and they collectively have had eight grandchildren. I am proud of my family, and consider my family, and their succeeding families, as my greatest achievement. My grandchildren who are old enough to know me call me Pop Pop. I have also had step children and step grandchildren. I have been the host father of various international high school students. Thus there are a number of young people who have called me Dad. I have sometimes been called the father of the Sudanese community in Rochester, New York. In China, some students and young people have considered me a likeable grandfather. I like these various labels. I am glad that my family is a broad extended family, spanning more than just my own personal family, whom I treasure and love.