Abstract: A composite roof structure, and a corresponding method of fabricating the structure, are disclosed which includes use of a layer of adhesive material (preferably a foamed, cellular adhesive such as polyurethane) along with a flexible membrane including a rubber-like sheet having a fleece-like matting secured to the underside thereof. The adhesive is preferably sprayed onto a roof substrate and prior to complete solidification thereof the membrane is pressed into the adhesive so that the matting becomes embedded therein.