Undoped GaInAs/zinc-doped InP structures grown by metal-organic chemical vapour deposition have been exposed to a RF hydrogen or deuterium plasma. Secondary ion mass spectrometry experiments show deuterium diffusion in both materials and the existence of a hydrogen-acceptor pairing effect in the p-type InP layer. After hydrogenation, the InP layer becomes highly resistive as a result of a strong passivation of acceptors by hydrogen. Hall effect and conductivity measurements performed on a lightly thermally reactivated InP layer indicate that the hole mobility is significantly higher than in the non-hydrogenated InP layer. This increase is attributed to a decrease of the ionised acceptor concentration under hydrogenation and is consistent with the existence of a pairing between the proton and the ionised acceptor giving rise to neutral Zn-H complexes. The relative thermal stability of Zn-H complexes in InP:Zn if compared to GaAs:Zn can be interpreted with the help of the microscopic model of these complexes, hydrogen being more tightly bonded to a phosphorus than to an arsenic atom.