The Church is the Mystical Body of Christ, the People of God. Those baptised are living members of the Church and continue here on earth the work of Christ.
The baptised do not have a relationship with the Church, they are the Church. They have a special relationship of love, obedience and faithfulness to Christ. It is this relationship of love towards Jesus that has encouraged Anglo Catholics to start their pilgrimage to heal the division started at the Reformation.
To understand better the nature of the Church we recommend the reading of Lumen Gentium. This is one of the major documents of Vatican II and is found on the list to the right of this post.