A composite porous membrane is a composite porous membrane, wherein a porous membrane B including a heat-resistant resin is laminated on the surface of a polypropylene resin of an outermost layer of a porous membrane A composed of at least one layer, wherein at least one of the outermost layers comprises the polypropylene resin. The composite porous membrane satisfies a particular range of peeling strength at the interface between the porous membrane A and the porous membrane B and a particular range of difference between air resistance of the whole composite porous membrane and air resistance of the porous membrane A, provided that the porous membrane A satisfies a particular range of average pore size and porosity.