The structure of block copolymers results from the interplay between weak intermolecular forces, typically in the order of k(B)T per molecule. This is particularly true for block copolymer thin films in the presence of chemically patterned surfaces, where the different contributions to the total free energy, the interfacial and bulklike terms, have comparable magnitudes. Here, we report on the structures formed by block copolymers films equilibrated between two chemically patterned surfaces with orthogonal stripes. Our experiments and simulations reveal that the domains are continuous through the film and the interface between domains resembles the Scherk's first minimal surface. The impact of chemical patterns on block copolymer morphologies and the underlying physics gives insight into the nanofabrication of complex nanostructures with directed self-assembly using two engineered boundary conditions, as opposed to only one.