Moiré superlattices of transition metal dichalcogenide (TMD) heterostructures give rise to rich excitonic phenomena associated with the interlayer twist angle. Theoretical calculations of excitons in such systems are typically based on model moiré potentials that mitigate the computational cost. However, predictive understanding of the electron-hole coupling dominating the excitations is crucial to realize the twist-induced modifications of the optical selection rules. In this work, we use many-body perturbation theory to evaluate the relation between twist angle and exciton properties in TMD heterostructures. We present an approach for unfolding excitonic states from the moiré Brillouin zone onto the separate-layer ones. Applying this method to a large-angle twisted MoS$_2$/MoSe$_2$ bilayer, we find that the optical spectrum is dominated by mixed electron–hole transitions with different momenta in the separate monolayers, leading to unexpected hybridization between interlayer and intralayer excitons. Our findings offer a design pathway for exciton layer-localization in TMD heterostructures.