Thick hydride vapor phase epitaxially grown orientation-patterned gallium phosphide (OPGaP) is a leading material for quasi-phase matching (QPM) frequency conversion in the mid- and longwave infrared (IR). This is due to its negligible two-photon absorption (2PA) in the convenient pumping range 1 – 1.7 μm, compared with the 2PA of some traditional QPM materials, such as GaAs. In this paper, we describe homo- and heteroepitaxial growth techniques aimed to produce hundreds of microns thick OPGaP on: 1) OPGaAs templates fabricated using an improved wafer-fusion process; 2) OPGaAs templates fabricated by using a molecular beam epitaxy (MBE) for sublattice polarity inversion, but one with and one without MBE regrowth after the inversion. Some of the advantages of the heteroepitaxial growth of OPGaP on OPGaAs templates include: 1) achieving good domain fidelity as a result of the significantly higher OPGaAs template quality; 2) eliminating the needs of using the poor quality commercially available GaP in the production of thick OPGaP material, and 3) suppression of the additional absorption band between 2 – 4 μm (which is due to incorporation of n-type impurities) and, in general, improvement of the IR transmittance in the entire IR region. Combining the advantages of the two most promising nonlinear materials, GaAs and GaP, will accelerate the development of high power, broadly tunable laser sources in the IR which, in addition, will be offered with higher device quality and at a reasonably lower unit cost.