Metallic hydrides represent a very interesting solution for hydrogen storage thanks to their capability to absorb hydrogen in a reversible way. Light metallic alloys recently developed may need the use of metallic films as protective barriers, and palladium nanofilms represent a very relevant example. In the present study we analyze with in situ surface X-ray diffraction the structure of about 20 monolayer thick Pd nanofilms electrodeposited onto Pt(111) before and after hydrogen electro-insertion and after hydrogen electro-desorption. The influence of the substrate on the pseudo-morphic character of the palladium deposit over about 10 palladium layers and on the structure evolution during the hydrogen insertion/desorption processes is demonstrated. After hydrogen insertion, an asymmetric expansion of the film, almost four times smaller in the surface plane with respect to the out of plane direction, is observed. The presence of two differently ordered regions in the hydride film and of a morphological irreversibility after hydrogen desorption is also shown