We investigate the effect of spin-orbit coupling on proximity-induced superconductivity in a normal metal attached to a superconductor. Specifically, we consider a heterostructure where the presence of interfaces gives rise to a Rashba spin-orbit coupling. The properties of the induced superconductivity in these systems are addressed within the tunneling Hamiltonian formalism. We find that the spin-orbit coupling induces a mixture of singlet and triplet pairing and, under specific circumstances, odd-frequency, even-parity, spin-triplet pairs can arise. We also address the effect of impurity scattering on the induced pairs and discuss our results in the context of heterostructures consisting of materials with spin-momentum locking.