A monolayer, bilayer, trilayer, or multilayer porous membrane having at least one layer that contains a thermoplastic resin and a polymer that is incompatible with the thermoplastic resin. One structure is a multilayer porous membrane where at least one internal layer of the multilayer porous membrane contains the thermoplastic resin and the polymer that is incompatible with the thermoplastic resin. Higher amounts of incompatible polymer may be used in an internal layer. This structure has improved properties, including improved puncture strength. Another structure includes at least one layer containing polyethylene and a polymer that is incompatible with polyethylene. The at least one layer containing polyethylene and a polymer that is incompatible with polyethylene may be an internal layer or an external layer. An internal layer may include more incompatible polymer than an external layer. The porous membranes may be used as battery separators. For example, they may be used as battery separators in secondary batteries such as lithium ion secondary batteries.