There are two way that families, kinship and descent connect. The first is through how they each are constructed. The second is through the function of each.
Descent is the means of tracking lineage from ancestors to the present day: your great-grandfather was an immigrant from Russia who fled because of social pressures being imposed after "Bloody Sunday" by Czar Nicholas II.
Kinship is the relationship that operates between people related to each other through the same lines of descent. Your cousin Marty is the son of your father's sister, who is your aunt, and whose mother, your grandmother, fled Russia as a little girl with her parents, your great-grandparents, after "Bloody Sunday."
Family is the units of immediate family, extended family and collateral family that have relationships of parentage, kinship or adoptive kinship through three or more generations in what may be collateral (i.e., collective) living accommodations. Mom and Pop adopt Jay and Mom gives birth to Joy, while Joy's paternal aunt and cousin (Joy's aunt's son) and grandmother come to live at Mom and Pop's large ranch and then comprise a collateral family group.
These definitions and examples show that family, kinship, and descent are connected through function, which is how individuals categorize and interact with relatives, and through construction.
As the adoptive example under "Family" illustrates, family and kinship are constructed socially: e.g., a social decision was made to expand the family range by adopting a new member with no lineage of descent.
This points out that the construction of descent differs definitively from the construction of family, including marriage, and kinship. While family, marriage and kinship are socially constructed, descent is a biological construction: descent is the passing on of genetic material to the next generation.