We perform first-principles, density-functional-theory calculations of the electronic structure for the layered bulk materials SnS and GeS which are of interest for photovoltaic applications. Band gap corrections are computed within the GW approximation to the electron self-energy. The resulting quasiparticle gaps in both SnS and GeS are in excellent agreement with the majority of existing experimental measurements. In order to better understand the possible use of GeS layers as a carrier-confining barrier within a SnS-based photovoltaic device, we compute the band offsets for different orientations of a SnS/GeS heterojunction. We find the valence band offsets to be almost independent of interfacial direction while the conduction band offsets show a strong anisotropy as a result of the variation in the band gap caused by epitaxial strain along the different directions.