A porous polymer sheet or membrane is provided with a thin coating of an electrically non-conductive ceramic composition and the coating conforms to all surfaces, including the pore surfaces, of the membrane. Such a coated membrane serves well, for example, as an intra-cell separator in a lithium ion battery. The coating increases the mechanical properties and thermal stability of the separator in battery operation and retains electrolyte. The coating may be formed by a two-step vapor-phase process in which atoms of one or more metals such as aluminum, calcium, magnesium, titanium, silicon and / or zirconium are deposited in a conformal layer on a workpiece surface. The metal atoms may then be reacted with ammonia, carbon dioxide, and or water to form their respective non-conductive nitrides, carbides, and / or oxides on the surface. The two-step process is repeated as necessary to obtain a ceramic material coating of desired thickness.