A composite membrane for selectively pervaporating a first liquid from a mixture comprising the first liquid and a second liquid. The composite membrane includes a porous substrate comprising opposite first and second major surfaces, and a plurality of pores. A pore-filling polymer is disposed in at least some of the pores so as to form a layer having a thickness within the porous substrate. The polymer is more permeable to the first liquid than the second liquid but not soluble in the first liquid or the second liquid. The composite membrane may be asymmetric or symmetric with respect to the amount of pore-filling polymer throughout the thickness of the porous substrate.