The present invention provides a composite porous membrane suited for a separator for a battery having excellent ion permeability, low pore blocking temperature, and high membrane breakage temperature by compositing resin porous membranes having different melting points (or softening points) without using a termocompression bonding method or a method of directly applying a solution to the substrate by using a composite porous membrane containing a porous membrane A of a resin having a melting point of 150.degree. C. or less and a porous membrane B of a resin having a glass transition temperature of more than 150.degree. C. integrated with the porous membrane A, wherein both a superficial side of the porous membrane B and an interfacial side with the porous membrane A of the porous membrane B have a three-dimensional network structure.