When pressed, I think most Christians would admit that there is an "invisible" unity of the Church. We as Christians are members of Christ's body and sealed by the Holy Spirit. That is the work of Christ and not of the church. Therefore we Christians are ontologically unified.
The real question comes up in regards to "visible" expressions of Christian unity. What shared characteristic makes any two congregations unified? There is no single answer, and I think different traditions would say different things. I'll propose this non-exhaustive list of possibilities for the most important manifestation of Christian unity:
- Orthodoxy (or common confession)
- Mode of baptism
- Charismatic practice
- Understanding of communion (or the sacraments in general)