or is there rather a way that they mutually build each other up to carry on the mission of the Church?
(I'd go with the latter of those two options!)
See how in my next article from the Catholic Telegraph!
The Decree on the Laity from Vatican II clearly picks up this theme as the Council Fathers state that all members of the Church are responsible for the building up of the Body of Christ. (#2) But the laity cannot fulfill this mission on their own, or independent of the ministerial priesthood: the clergy and the laity must work together!