A separator-electrolyte layer product for use in a lithium battery, comprising: (a) a porous thin-film separator selected from a porous polymer film, a porous mat, fabric, or paper made of polymer or glass fibers, or a combination thereof, wherein the separator has a thickness less than 500 μm; and (b) a non-flammable quasi-solid electrolyte containing a lithium salt dissolved in a liquid solvent up to a concentration no less than 3 M; wherein the porous thin-film separator is coated with the quasi-solid electrolyte so that the layer product exhibits a vapor pressure less than 0.01 kPa when measured at 20° C., a vapor pressure less than 60% of the vapor pressure of the liquid solvent alone, a flash point at least 20 degrees Celsius higher than a flash point of the first liquid solvent alone, a flash point higher than 150° C., or no detectable flash point.