The conjugal community is established upon the consent of the spouses. Marriage and the family are ordered to the good of the spouses and to the procreation and education of children. the love of the spouses and the begetting of children create among members of the same family personal relationships and primordial responsibilities. CCC 2201
A man and a woman united in marriage form a family together with their children. God instituted the family and endowed it with its fundamental constitution. Marriage and the family are ordered to the good of the spouses and to the procreation and education of children. Members of the same family establish among themselves personal relationships and primary responsibilities. In Christ, the family becomes the domestic church because it is a community of faith, of hope, and of charity. (#456)
The Catechism Companion Vol III has some good commentary on this:
Everyone in a family, including parents and children, are "equal in dignity," reflecting the value of all individuals created in God's image (CCC 2203)... Families have imperfections, but they are still called within the Church to witness to the gospel. In the Church, the family is meant to point toward the Trinity. Families contribute to the growth of the Church primarily through friendships and family connections. Families and friendships play an important role in evangelizing, highlighting the importance of self-sacrificial relationships. (p. 86)
Finally, Cardinal Burke has a great video on the family as a little church: