A method for making a porous material, includes melt-blending two or more non-miscible polymers to obtain a co-continuous melt, solidifying the melt to obtain a solid mass consisting of two co-continuous polymer phases, and selectively extracting one of the co-continuous phases thereby creating within the solid mass an essentially continuous pore network having an internal surface. The method further includes replicating the internal surface of the pore network within the solid mass by coating the internal surface with successive layers of materials, and selectively extracting the solid mass without extracting the layers of materials, to thereby yield the product porous material, formed of the layers of materials. The material has a void fraction higher than about 75%, and mainly having essentially fully interconnected sheath-like non-spherical pores and essentially non-fibrous walls.