If you go a little further you’ll see it applies to both the church and the family.
Ephesians 5:32 This is a great mystery, and I am applying it to Christ and the church. 33 Each of you, however, should love his wife as himself, and a wife should respect her husband.
This is what I learned from catechism. The family unit made up of biological family members the father, the mother and children if any, is called the domestic church. Then there are parish churches, etc.led by our spiritual leaders, the priests, but we are also apart of the bigger Universal Church family. So it’s in reference to both.
The body of Christ is the members of the Universal Church which is the same as the bride of Christ. The bride of Christ is mentioned in Revelation as meeting the bridegroom (Jesus). We as a church are part of the body of Christ. We are the body and Christ is the head. The bride meets the bridegroom because it is a union made by God, perfect and Holy in every way.
In the following scripture the body refers to the church, and we walk by faith not sight but one day all will be revealed to us.
2 Corinthians 5:6 So we are always confident; even though we know that while we are at home in the body we are away from the Lord— 7 for we walk by faith, not by sight.
Of course the body of Christ is also the Holy Eucharist that we share as the body of Christ. Jesus came once as a baby through Mary, and now the Body of Jesus is present as the Holy eucharist, and Jesus will come again as the Second coming to receive the body of Christ-us so that we will be glorified with Christ into One Body of Christ.
This is what I’ve come to learn, correct me if anyone knows better like a priest,