This invention provides a novel battery structure that, in some variations, utilizes a mixed lithium-ion and electron conductor as part of the separator. This layer is non-porous, conducting only lithium ions during operation, and may be structurally free-standing. Alternatively, the layer can be used as a battery electrode in a lithium-ion battery, wherein on the side not exposed to battery electrolyte, a chemical compound is used to regenerate the discharged electrode. This battery structure overcomes critical shortcomings of current lithium-sulfur, lithium-air, and lithium-ion batteries.