Strong light-matter interactions in van der Waals heterostructures (vdWHs) made of two-dimensional (2D) transition metal dichalcogenides (TMDs) provide a fertile ground for optoelectronic applications. Of particular interest are photoexcited interlayer electron-hole pairs, where electrons and holes are localized in different monolayers. Here, we present an ab initio quantum transport framework relying on maximally localized Wannier functions and the nonequilibrium Green's functions to explore light-matter interactions and charge transport in 2D vdWHs from first principles. Electron-photon scattering is accurately taken into account through dedicated self-energies. As testbed, the behavior of a MoSe₂−WSe₂ PIN photodiode is investigated under the influence of a monochromatic electromagnetic signal. Interlayer electron-hole pair generations are observed even in the absence of phonon-assisted processes. The origin of this phenomenon is identified as the delocalization of one valence band state over both monolayers composing the vdWH.