The present invention relates to composite roof structures and their preparation. The composite roof structure is prepared by applying a one-part, moisture curable, foaming, polyurethane adhesive composition to the roof deck, placing the roofing material in contact with the adhesive composition, and allowing the adhesive mixture to foam, fill, and cure. If multiple layer of the roofing material are used to form the composite roof structure, then the above procedure may be used to adhere each of the roofing material layers.