Two and three-dimensional (2D/3D) hybrid materials have the potential to advance communication and sensing technologies by enabling new or improved device functionality. To date, most 2D/3D hybrid devices utilize mechanical exfoliation or post-synthesis transfer, which can be fundamentally different from directly synthesized layers that are compatible with large scale industrial needs. Therefore, understanding the process/property relationship of synthetic heterostructures is priority for industrially relevant material architectures. Here we demonstrate the scalable synthesis of molybdenum disulfide (MoS2) and tungsten diselenide (WSe2) via metal organic chemical vapor deposition (MOCVD) on gallium nitride (GaN), and elucidate the structure, chemistry, and vertical transport properties of the 2D/3D hybrid. We find that the 2D layer thickness and transition metal dichalcogenide (TMD) choice plays an important role in the transport properties of the hybrid structure, where monolayer TMDs exhibit direct tunneling through the layer, while transport in few layer TMDs on GaN is dominated by p-n diode behavior and varies with the 2D/3D hybrid structure. Kelvin probe force microscopy (KPFM), low energy electron microscopy (LEEM) and X-ray photoelectron spectroscopy (XPS) reveal a strong intrinsic dipole and charge transfer between n-MoS2 and p-GaN, leading to a degraded interface and high p-type leakage current. Finally, we demonstrate integration of heterogeneous 2D layer stacks of MoS2/WSe2 on GaN with atomically sharp interface. Monolayer MoS2/WSe2/n-GaN stacks lead to near Ohmic transport due to the tunneling and non-degenerated doping, while few layer stacking is Schottky barrier dominated.