TECHNOLOGY FOCUS - POLYMERS - Preferred Component: The membrane comprises a first microporous membrane layer and second microporous membrane layer, where the layers are in planar contact. The first microporous membrane layer comprises 30-65 wt.% of a first polyethylene having weight average molecular weight (Mw) of less than 1x 106; 5-15 wt.% of a second polyethylene having Mw of greater than or equal to 1x 106; 20-40 wt.% of a first polypropylene having Mw of greater than or equal to 0.8x 106 and heat of fusion ( Delta Hm) of greater than or equal to 80 J/g; and 10-30 wt.% of a second polypropylene having an Mw of less than 0.8x 106 and a Delta Hm of greater than or equal to 80 J/g. The second microporous membrane layer comprises 60-90 wt.% of a first polyethylene having Mw of less than 1x 106; and 10-40 wt.% of a second polyethylene having an Mw of greater than or equal to 1x 106. The first polyethylene and the second polyethylene of the first layer have molecular weight distribution (MWD) of 2-10. The first polypropylene has MWD of 1.5-10. The second polypropylene has MWD of 2-20. The first polyethylene of the second layer has MWD of 2-10. The second polyethylene of the second layer has MWD of 2-10. Each of the first polyethylene and the second polyethylene is ethylene homopolymer or ethylene/ alpha -olefin copolymer. Each of the first polypropylene and the second propylene is propylene homopolymer or propylene/ alpha -olefin copolymer. Preferred Properties: The first layer has a first thickness and the second layer has a second thickness, where ratio of the first thickness to the second thickness is 10:90-75:25. The membrane has a thickness of greater than or equal to 3 mu m, melt down temperature of greater than or equal to 150 degrees C, an air permeability of less than or equal to 400 seconds/100 cm3, a porosity of 25-80%, a tensile strength of greater than or equal to 40000 kPa in planar direction(s), a tensile elongation of greater than or equal to 100%, a heat shrinkage of less than or equal to 12% in planar direction(s), a thickness variation ratio after heat compression of less than or equal to 10%, an electrolytic solution absorption speed of greater than or equal to 1.5, or a surface roughness of greater than or equal to 3x 102 nm. Preferred Method: The method further comprises a heat-setting treatment step after stretching the cooled extrudate, where the stretched sheet is heat-set at a stretching temperature plus minus 5 degrees C; a heat roll treatment step where the stretched sheet contacts a heated roller at a temperature from the crystal dispersion temperature of the polyolefin composition to the melting point +10 degrees C of the polyolefin composition; and a hot solvent treatment step where the stretched sheet is contacted with a hot solvent. The method also comprises heat-setting treatment step following removal of portion(s) of the diluent from the stretched sheet, where the membrane is heat-set at a temperature of the stretching temperature +5 degrees C; and a cross-linking step where the heat-set membrane is cross-linked by ionizing radiation rays selected from one or more of alpha -rays, beta -rays, gamma -rays, or electron beams. The method may further comprise a hydrophilizing treatment step following heat-setting the stretched membrane product, where the heat-set microporous membrane is made more hydrophilic by a monomer-grafting treatment, a surfactant treatment, or a corona-discharging treatment; and/or a surface-coating treatment step, where the heat-set microporous membrane is coated with one or more of a porous polypropylene, a porous fluororesin, a porous polyimide, or a porous polyphenylene sulfide. EXAMPLE - A first polyolefin composition comprising 40 wt.% first polyethylene resin having weight average molecular weight (Mw) of 5.6x l05 and molecular weight distribution (MWD) of 4.05; 10 wt.% second polyethylene resin having Mw of 1.9x 106 and MWD of 5.09; 37.5 wt.% first polypropylene resin having Mw of 1.1x 106, heat of fusion of 114 J/g and MWD of 5; and 12.5 wt.% second polypropylene resin having Mw of 6.6x 105, heat of fusion of 103.3 J/g and MWD of 11.4, was prepared by dry-blending. The resultant first polyolefin composition (25 pts.wt.) was charged into a strong-blending double-screw extruder. Then, liquid paraffin (75 pts.mass) was supplied to the double-screw extruder via a side feeder. Melt-blending was conducted at 210 degrees C and 200 rpm. A second polyolefin solution comprising 80 wt.% first polyethylene resin having Mw of 5.6x l05 and MWD of 4.05; and 20 wt.% second polyethylene resin having Mw of 1.9x 106 and MWD of 5.09, was prepared in the same manner as above. The resultant second polyolefin composition (30 pts.wt.) was then charged into a strong-blending double-screw extruder, and liquid paraffin (70 pts.mass) was supplied. The polyethylene resin in the first and second compositions had a melting point of 135 degrees C and a crystal dispersion temperature of 100 degrees C. The first and second polyolefin solutions were supplied from their respective double-screw extruders to a three-layer-extruding T-die, and extruded to form an extrudate or laminate of first polyolefin solution layer/second polyolefin solution layer/first polyolefin solution layer at a layer thickness ratio of 10/80/10. The extrudate was cooled while passing through cooling rollers at 20 degrees C, to form a three-layer gel-like sheet which was simultaneously biaxially stretched at 115 degrees C to a 5-fold magnification in longitudinal and transverse directions. The stretched three-layer gel-like sheet was fixed to an aluminum frame, immersed in methylene chloride bath at 25 degrees C to remove liquid paraffin with vibration of 100 rpm for 3 minutes, and dried by air flow at room temperature. The dried membrane was re-stretched to a 1.4-fold magnification in transverse direction at 12 degrees C. The re-stretched membrane which remained fixed to the batch-stretching machine, was heat-set at 125 degrees C for 10 minutes to produce a three-layer microporous membrane.