A self-adhering underlayment for tile roofing assemblies has been issued a patent. The underlayment comprises a dual-compound composite sheet including a carrier sheet with a front side and a backside. The carrier sheet is sandwiched between a top layer and a bottom layer. The top layer is comprised of a mixture of: (a) polypropylene modifiers comprised of isotactic polypropylene, ethylene-propylene copolymer, atactic polypropylene and polyethylene, (b) filler and (c) asphalt. The bottom layer is comprised of self-adhesive compound made of a mixture of: (a) styrene-butadiene-styrene copolymer, (b) styrene-isoprene-styrene copolymer, (c) hydrocarbon tackifying resins and (d) asphalt. The top and bottom layers form opposite-facing upper and lower surfaces.