Two-dimensional transition-metal dichalcogenides (TMDCs) have recently emerged as a promising class of materials. A fascinating aspect of these atomically thin crystals is the possibility of combining different TMDCs into heterostructures. For several TMDC combinations, a staggered band alignment occurs, so that optically excited electron-hole pairs are spatially separated into different layers and form interlayer excitons (IEX). Here, we report on time-resolved, low-temperature photoluminescence (PL) of these IEX in a MoSe₂-WSe₂ heterostructure. In the time-resolved measurements, we observe indications of IEX diffusion in an inhomogeneous potential landscape. Excitation-density-dependent measurements reveal a dipolar, repulsive exciton-exciton interaction. PL measurements in applied magnetic fields show a giant valley-selective splitting of the IEX luminescence, with an effective g factor of about -15. This large value stems from the alignment of K+ and K-valleys of the constituent monolayers in our heterostructure, making intervalley transitions optically bright, so that contributions to the field-induced splitting arising from electron and hole valley magnetic moments add up. This giant splitting enables us to generate a near-unity valley polarization of interlayer excitons even under linearly polarized excitation by applying sufficiently large magnetic fields.