  Van der Waals heterostructures (vdWH) provide an ideal playground for
exploring light-matter interactions at the atomic scale. In particular,
structures with a type-II band alignment can yield detailed insight into free
carrier-to-photon conversion processes, which are central to e.g. solar cells
and light emitting diodes. An important first step in describing such processes
is to obtain the energies of the interlayer exciton states existing at the
interface. Here we present a general first-principles method to compute the
electronic quasi-particle (QP) band structure and excitonic binding energies of
incommensurate vdWHs. The method combines our quantum electrostatic
heterostructure (QEH) model for obtaining the dielectric function with the
many-body GW approximation and a generalized 2D Mott-Wannier exciton model. We
calculate the level alignment together with intra and interlayer exciton
binding energies of bilayer MoS$_2$/WSe$_2$ with and without intercalated hBN
layers, finding excellent agreement with experimental photoluminescence
spectra. Comparison to density functional theory calculations demonstrate the
crucial role of self-energy and electron-hole interaction effects.
