Abstract: Disclosed is a membrane with one or more dry-process porous layers that comprise (1) a polyolefin and (2) a product formed by reacting two components, which may be a compound with one or more carboxy groups and a compound with one or more epoxy groups. The product may be a reaction network, a three-dimensional reaction network, or a cross-linked network The resulting membrane has improved strength, reduced splittiness, or both improved strength and reduced splittiness. The membrane may be used in a battery, capacitor, HVAC, filtering device, or textile. Methods for making the membrane are also disclosed.