The present application discloses a composite membrane comprising (a) a support member that has a plurality of pores extending through the support member and (b) a cross-linked copolymer comprising (i) a cationic monomer and an anionic monomer and/or (ii) a zwitterionic monomer, which cross-linked copolymer fills the pores of the support member, the cross-linked copolymer having a permeability for a fluid that is dependent on the polarity of the fluid, wherein the permeability increases with increasing polarity.The present application also discloses a process for the preparation of the composite membrane, a pervaporation apparatus comprising the composite membrane, and methods for the use of the composite material in separation and dehydration processes.