Wetting phenomena are theoretically studied for a slit pore or slab geometry between two structured surfaces which contain stripes of lyophilic surface domains. Two different approaches are used and compared: Monte Carlo simulations of lattice gas models and minimization methods applied to effective interface models. Both types of calculations show that the wetting liquid often attains anvil-like bridges which are not translationally invariant parallel to the surface stripes. As a control parameter such as the Liquid volume or the surface separation is changed, these bridges undergo morphological wetting transitions to symmetric or asymmetric channel states.