We investigate the connection between biphoton states involving photons in product modes of their spin and orbital degrees of freedom and those involving photons in hybrid spin-orbit modes, as mediated by Hong-Ou-Mandel interference (HOMI) in an asymmetric Mach-Zehnder interferometer. We predict that two input photons in balanced superposition states of both their spin and orbital degrees of freedom will exhibit HOMI while undergoing a simultaneous mode conversion from product spin-orbit input modes to hybrid output modes bearing orbital angular momentum. These hybrid outputs contain a spatially varying polarization structure which may be controllably rotated about the photonic beam axis by varying the relative phase between the vertical and horizontal components of each input photon's polarization. Additionally, a type of coupling of the spin and orbital degrees of freedom is exhibited in this system: the transverse spatial profile of the output photons may be continuously manipulated by tuning the polarization parameters of the input photons, in such a way that the HOMI between the photons remains stable. An interesting corollary to this work is the possibility of demonstrating in a simple experimental system that HOMI may occur between distinguishable input modes.