A thin, freestanding, microporous polyolefin web with good heat resistance and dimensional stability includes an inorganic surface layer. A first preferred embodiment is a microporous polyolefin base membrane in which colloidal inorganic particles are present in its bulk structure. Each of second and third preferred embodiments is a thin, freestanding microporous polyolefin web that has an inorganic surface layer containing no organic hydrogen bonding component for the inorganic particles. The inorganic surface layer of the second embodiment is achieved by hydrogen bonding with use of an inorganic acid, and the inorganic surface layer of the third embodiment is achieved by one or both of hydrogen bonding and chemical reaction of the surface groups on the inorganic particles.