Described herein is a multilayer microporous film or membrane that may exhibit improved properties, including improved dielectric break down and strength, compared to prior monolayer or tri-layer microporous membranes of the same thickness. The preferred multilayer microporous membrane comprises microlayers and one or more lamination interfaces or barriers. Also disclosed is a battery separator or battery comprising one or more of the multilayer microporous films or membranes. The inventive battery and battery separator is preferably safer and more robust than batteries and battery separators using prior monolayer and tri-layer microporous membranes. Also, described herein is a method for making the multilayer microporous separators, membranes or films described herein.