In what ways is the Church like a family?

Individual families are connected through the Holy Family as a Church family.  CCC 541 and 542 says that this is God's plan.

A person who enters the Church by faith and Baptism becomes a disciple of Christ. By doing the will of the Father in heaven, he forms part of Jesus’ “true family” (cf. Mt. 12:49). “Becoming a disciple of Jesus means accepting the invitation to belong to God’s family” (Catechism, no. 2233, original emphasis). If after Baptism the person falls away from the Church, then by repentance and conversion he returns like the prodigal son “to God and to the bosom of his family, which is the Church” (Catechism, no. 1439).

Gadenz, P. (1998). The Church as the Family of God. In S. Hahn & L. J. Suprenant Jr. (Eds.), Catholic for a Reason: Scripture and the Mystery of the Family of God (p. 73). Steubenville, OH: Emmaus Road Publishing.

Not much to add to the excellent reply above.  We are all God's Creatures - His Creation.  We, who have been baptized, are God's Children.  This makes us siblings - brothers and sisters.