In a preferred embodiment, a membrane for use as an underlayment includes a basemat, which includes at least three plies, a ply of a meltblown polymer sandwiched between two plies of spunbond polymer; and a flexible coating applied to the basemat, the coating having a cementitious hydraulic component, a polymer comprising a water-soluble, film-forming polymer; and water. The finished membrane is flexible. Another embodiment for an underlayment for use underneath ceramic tiles includes a basemat and a coating of a set hydraulic component less than ⅛″ inches thick. A method of making the flexible membrane includes assembling components including a hydraulic component, a water-soluble, film-forming polymer and water, then mixing them to form a coating. A basemat is provided onto which the coating is applied over a flexible surface or no surface. After coating at least one face of the basemat, the coating is dried to form the membrane.