Composite membranes comprising a layer having first and second microporous surfaces and a bulk between the surfaces, the bulk comprising a first set of pores having outer rims, and a second set of pores connecting the rims, and a polymer matrix supporting the first set of pores; and, a second layer having first and second porous surfaces and a second bulk between the porous surfaces, wherein the second bulk comprises a fibrous matrix; or, first and second microporous surfaces and a second bulk between the microporous surfaces, the second bulk comprising: a third set of pores having outer rims and a fourth set of pores connecting the rims, and a polymer matrix supporting the third set of pores; a third set of pores prepared by phase inversion; or, a fibrous matrix; or, a third set of pores prepared by stretching, track etching or e-beam, are disclosed.