While monolayer forms of two-dimensional materials are well characterized both experimentally and theoretically, properties of bilayer heterostructures are not nearly so well known. We employ high-accuracy linear-scaling density functional theory calculations utilizing nonlocal van der Waals functionals to explore the possible constructions of the MoS2/MoSe2 interface. Utilizing large supercells, we vary rotation, translation, and separation of the layers without introducing unrealistic strain. The energy landscape shows very low variations under rotation, with no strongly preferred alignments. By unfolding the spectral function into the primitive cells, we show that the monolayers are more independent than in homo-bilayers and that the electronic band structure of each layer is tunable through rotation, thus influencing hole effective masses.