Asymmetric composite membranes and methods for their preparation are disclosed. The membranes comprise a cross-linked poly(vinyl alcohol) polymer coated on a film of cross-linked sulfonated poly(ether ether ketone) adhered to a sheet of hydrophilicitized microporous polyolefin. The microporous polyolefin is typically microporous poly(ethylene). The membranes have improved selectivity with the regard to the rejection of solutes in reverse osmosis and ultrafiltration applications.