An RF-transparent sunshield membrane covers an antenna reflector such as a parabolic dish. The blanket includes a single dielectric sheet of polyimide film 1/2-mil thick. The surface of the film facing away from the reflector is coated with a transparent electrically conductive coating such as vapor-deposited indium-tin oxide. The surface of the film facing the reflector is reinforced by an adhesively attached polyester or glass mesh, which in turn is coated with a white paint. In a particular embodiment of the invention, polyurethane paint is used. In another embodiment of the invention, a layer of paint primer is applied to the mesh under a silicone paint, and the silicone paint is cured after application for several days at room temperature to enhance adhesion to the primer.