A porous asymmetric membrane comprises a hydrophobic polymer comprising a poly(phenylene ether) or poly(phenylene ether) copolymer; and a polymer additive. A separation module can be fabricated from the porous asymmetric membrane. A method of forming the porous asymmetric membrane comprises: dissolving a hydrophobic polymer comprising a poly(phenylene ether) or poly(phenylene ether) copolymer and, a polymer additive in a water-miscible polar aprotic solvent to form a porous asymmetric membrane-forming composition; and phase-inverting the porous asymmetric membrane forming-composition in a first non-solvent composition to form the porous asymmetric membrane. The polymer additive comprises hydrophilic functional groups, copolymerized hydrophilic monomers, or blocks of hydrophilic monomer repeat units. For example, the polymer additive can comprise a hydrophilic polymer or amphiphilic polymer. The porous asymmetric membrane can be a flat membrane or hollow fiber.