The present invention relates to a support structure/membrane composite device which includes a support structure, such as a radially expandable stent, a porous non-textile polymeric membrane adjacent to said stent and a thermoplastic anchor means attaching said stent to said porous non-textile polymeric membrane. The porous non-textile polymeric membrane is preferably made from expandable fluoropolymer materials. The anchoring means is a thermoplastic material which is dissolvable at the interface between the support structure and membrane by a suitable solvent which wets the membrane surface and deposits the thermoplastic material within the pores of the membrane. Methods of preparing the device are also disclosed.