Because of the chemical inertness of two dimensional (2D) hexagonal-boron nitride (h-BN), few atomic-layer hBN is often used to encapsulate air-sensitive 2D crystals such as black phosphorus (BP). However, the effects of h-BN on Schottky barrier height, doping, and contact resistance are not well-known. Here, we investigate these effects by fabricating h-BN encapsulated BP transistors with cobalt (Co) contacts. In sharp contrast to directly Co contacted p-type BP devices, we observe strong n-type conduction upon insertion of the h-BN at the Co/BP interface. First-principles calculations show that this difference arises from the much larger interface dipole at the Co/h-BN interface compared to the Co/BP interface, which reduces the work function of the Co/h-BN contact. The Co/h-BN contacts exhibit low contact resistances (similar to 4.5 k Omega) and are Schottky barrier-free. This allows us to probe high electron mobilities (4,200 cm(2)/(Vs)) and observe insulator metal transitions even under two-terminal measurement geometry.