The materials of adjoining porous metal substrate (12), oxide (14), and Pd-alloy membrane (16) layers of a composite, H2--separation palladium membrane (10) have respective thermal expansion coefficients (TEC) which differ from one another so little as to resist failure by TEC mismatch from thermal cycling. TEC differences (20, 22) of less than 3 .mu.m/(m.k) between materials of adjacent layers are achieved by a composite system of a 446 stainless steel substrate, an oxide layer of 4 wt % yittria-zirconia, and a 77 wt % Pd-23 wt % Ag or 60 wt % Pd-40 wt % Cu, membrane, having TECs of 11, 11, and 13.9 .mu.m/(m.k), respectively. The Intermediate oxide layer comprises particles forming pores having an average pore sizeless than 5 microns, and preferably less than about 3 microns, in thickness.
 The U.S. Government has a paid-up license in this invention and the right in limited circumstances to require the patent owner to license others on reasonable terms as provided for by the terms of (contract No. DE-FC36-02AL67628) awarded by the Department of Energy.