The solubility of hydrogen in niobium films (100--3000 A\r{}) and multilayers of Nb and Pd (20--130 A\r{}) has been studied as a function of film thickness by resistivity and x-ray measurements. The H concentration in solid solution was observed to be greatly enhanced, by a factor of more than 40, as the Nb films were made thinner. This suggests a dependence of the phase diagram on film thickness, with a depression of the Nb-H critical temperature for films thinner than 1200 A\r{}, but approaching the bulk values for thick films (tg2200 A\r{}). Similar results were observed in Nb-Pd multilayers.