A cross-linked polymer containing pendant molecules attached to the polymer framework is shown to form flexible and low-cost membranes, to be a solid Lit electrolyte up to 270 degrees C, much higher than those based on poly(ethylene oxide), to be wetted by a metallic lithium anode, and to be not decomposed by the metallic anode if the anions of the salt are blocked by a ceramic electrolyte in a polymer/ceramic membrane/polymer sandwich electrolyte (PCPSE). In this sandwich architecture, the double-layer electric field at the Li/polymer interface is reduced due to the blocked salt anion transfer. The polymer layer adheres/wets the lithium metal surface and makes the Li-ion flux at the interface more homogeneous. This structure integrates the advantages of the ceramic and polymer. With the PCPSE, all-solid-state Li/LiFePO4 cells showed a notably high Coulombic efficiency of 99.8-100% over 640 cycles.