A multi-layer, microporous polyolefin membrane having at least two layers comprising a first microporous layer containing a first microporous layer material and a second microporous layer containing a second microporous layer material, wherein (a) the first microporous layer material comprises one of (i) a first polyethylene having an Mw that is less than 1x10 6; (ii) the first polyethylene and a second polyethylene having a Mw of at least 1 x 10 6, wherein the second polyethylene is present in an amount that does not exceed 7% by mass based on the combined mass of the first and second polyethylene; (iii) the first polyethylene and a first polypropylene, wherein the amount of the polypropylene does not exceed 25% by mass based on the combined mass of the first polyethylene and the first polypropylene; or (iv) the first polyethylene, the second polyethylene, and the first polypropylene, wherein the first polypropylene is present in an amount that does not exceed 25% by mass based on the combined mass of the first polyethylene, the second polyethylene, and the first polypropylene, and wherein the second polyethylene is present in an amount that does not exceed 7% by mass based on the combined mass of the first and second polyethylene; (b) the second microporous layer material comprises one of (i) a fourth polyethylene having an Mw of at least 1x10 6; or (ii) a third polyethylene having an Mw that is less than 1x10 6 and the fourth polyethylene, wherein the fourth polyethylene is present in an amount of at least 8% by mass based on the combined mass of the third and fourth polyethylene; and (c) the first microporous layer material has a pore size distribution curve obtained by mercury intrusion porosimetry with at least two peaks. (a) the first microporous layer material comprises one of (i) a first polyethylene having an Mw that is less than 1x10 6; (ii) the first polyethylene and a second polyethylene having a Mw of at least 1 x 10 6, wherein the second polyethylene is present in an amount that does not exceed 7% by mass based on the combined mass of the first and second polyethylene; (iii) the first polyethylene and a first polypropylene, wherein the amount of the polypropylene does not exceed 25% by mass based on the combined mass of the first polyethylene and the first polypropylene; or (iv) the first polyethylene, the second polyethylene, and the first polypropylene, wherein the first polypropylene is present in an amount that does not exceed 25% by mass based on the combined mass of the first polyethylene, the second polyethylene, and the first polypropylene, and wherein the second polyethylene is present in an amount that does not exceed 7% by mass based on the combined mass of the first and second polyethylene; (i) a first polyethylene having an Mw that is less than 1x10 6; (ii) the first polyethylene and a second polyethylene having a Mw of at least 1 x 10 6, wherein the second polyethylene is present in an amount that does not exceed 7% by mass based on the combined mass of the first and second polyethylene; (iii) the first polyethylene and a first polypropylene, wherein the amount of the polypropylene does not exceed 25% by mass based on the combined mass of the first polyethylene and the first polypropylene; or (iv) the first polyethylene, the second polyethylene, and the first polypropylene, wherein the first polypropylene is present in an amount that does not exceed 25% by mass based on the combined mass of the first polyethylene, the second polyethylene, and the first polypropylene, and wherein the second polyethylene is present in an amount that does not exceed 7% by mass based on the combined mass of the first and second polyethylene; (b) the second microporous layer material comprises one of (i) a fourth polyethylene having an Mw of at least 1x10 6; or (ii) a third polyethylene having an Mw that is less than 1x10 6 and the fourth polyethylene, wherein the fourth polyethylene is present in an amount of at least 8% by mass based on the combined mass of the third and fourth polyethylene; and (i) a fourth polyethylene having an Mw of at least 1x10 6; or (ii) a third polyethylene having an Mw that is less than 1x10 6 and the fourth polyethylene, wherein the fourth polyethylene is present in an amount of at least 8% by mass based on the combined mass of the third and fourth polyethylene; and (c) the first microporous layer material has a pore size distribution curve obtained by mercury intrusion porosimetry with at least two peaks.