Monolayer transition metal dichalcogenides integrated in optical microcavities host exciton-polaritons as a hallmark of the strong light-matter coupling regime. Analogous concepts for hybrid light-matter systems employing spatially indirect excitons with a permanent electric dipole moment in heterobilayer crystals promise realizations of exciton-polariton gases and condensates with inherent dipolar interactions. Here, we implement cavity-control of interlayer excitons in vertical MoSe₂-WSe₂ heterostructures. Our experiments demonstrate the Purcell effect for heterobilayer emission in cavity-modified photonic environments, and quantify the light-matter coupling strength of interlayer excitons. The results will facilitate further developments of dipolar exciton-polariton gases and condensates in hybrid cavity – van der Waals heterostructure systems.