A composite roof structure, and a corresponding method of fabricating the structure, are disclosed which includes use of a layer of non-cellular adhesive material (preferably a two-component non-cellular polyurea polyurethane adhesive material), roof insulation panels, along with a flexible roof membrane, preferably made of thermoplastic olefin rubber, including a rubber-like sheet having a fleece-like matting secured to the underside thereof. The non-cellular adhesive is preferably sprayed onto a roof substrate and prior to complete solidification thereof the roof membrane or roof insulation is pressed into the adhesive so that the matting becomes embedded therein.