Thin layers of a mixed composition are deposited on a porous substrate by chemical vapor deposition in an inert atmosphere at high temperature. The resulting membrane has excellent stability to water vapor at high temperatures. An exemplary membrane comprises an amorphous mixed-element surface layer comprising silica and at least one oxide of additional element, an optional porous substrate on which said surface layer is deposited, and a porous support on which said substrate or mixed-element surface layer is deposited, wherein the permeance of the membrane is higher than 1×10mol msPaand the selectivity of H₂ over CO, CO₂, and CH₄ is larger than 100, and wherein the H₂ permeance of the membrane after exposure to a stream containing 60 mol % water vapor at 673 K for 120 h is at least 50% of its initial H₂ permeance.