We present consistent theoretical studies of optically heterodyned polarization interferometry (OHPI) with noncollinear arbitrary polarized interacting beams in the framework of the cubic nonlinear optical susceptiblity formalism. Our theoretical treatment is based on the covariant tensorial approach introduced by F I Fedorov. We were able to derive the analytical expressions for the detected OHPI signal. Different methods for measuring the nonlinear susceptibility are also suggested.