We propose and theoretically analyze a new scheme for generating hyper-entangled photon pairs (EPPs) in a system of polaritons in coupled planar microcavities. Starting from a microscopic model, we evaluate the relevant parametric scattering processes and numerically simulate the phonon-induced noise background under continuous-wave excitation. Our results show that, compared to other polariton entanglement proposals, our scheme enables the generation of photon pairs that are entangled in both the path and polarization degrees of freedom, and simultaneously leads to a strong reduction in the photoluminescence noise background. This can significantly improve the fidelity of the EPPs under realistic experimental conditions.