Abstract: A method of making a self-inflating air mattress comprising an open cell foam core enclosed within, and bonded to, upper and lower sheets. Each sheet is made by heat laminating to an outer substantially nonstretching fiber layer an intermediate solid polymer film layer to which is then heat laminated an inner solid polymer film layer having a melting temperature at which the intermediate film layer is structurally stable. The sheets are pressed against the foam core by heated platens, and afterwards cooled. These particular sheets form a reliable bond and alleviate a problem of creating air leaks through the intermediate film layer.