A study is presented of the self-assembly of a lamella-forming blend of a diblock copolymer and its respective homopolymers on periodically patterned substrates consisting of square arrays of spots, that preferentially attract one component, as a function of pattern dimensions and film thickness. The blend morphology follows the pattern at the substrate and forms a single quadratically perforated lamella (QPL). At intermediate film thicknesses necks connect this QPL to the film surface, resulting in a bicontinuous morphology. The necks do not register with the underlying square lattice but exhibit a substantial amount of hexagonal short-range order. For thicker films we observe bicontinuous morphologies consisting of parallel lamellae with disordered perforations. These results demonstrate a promising strategy for the fabrication of complex interfacial nanostructures from two-dimensional chemically patterned templates.