A fire-resistant polymeric membrane includes a polymer layer such as PVC, TPO, or EPDM affixed to a carbon fiber composite. The carbon fiber composite includes one or two layers of non-woven carbon fibers and at least one of an inert fiber mat or a metal foil layer, wherein the metal foil layer has a melting temperature of at least about 660° C. The present invention also provides an underlayment, wherein the underlayment is formed from one or more fibrous carbon layers affixed to at least one of an inert fiber mat or a metal foil having a melting temperature greater than 660° C.