A composite structure (12) that includes a first layer that includes a membrane (16) having a first melting point and a plurality of structural elements and a second layer that includes a thermoplastic material (32) having a second melting point that is lower than the first melting point, wherein at least a portion of the thermoplastic material (34) is at least one partially melted to flow around at least one structural element of the plurality of structural elements of the membrane (16) prior to resolidification to attach the first layer (16) to the second layer (32). The membrane (16) can be oleophobic or oleophilic and preferably includes expanded polytetrafluoroethylene. The thermoplastic material (32) can be of virtually any type and can be either hydrophobic or hydrophilic.