Separator-electrode assemblies (SEAs) comprising a porous electrode useful as a positive or negative electrode in a lithium battery and a separator layer applied to this electrode, the separator layer being an inorganic separator layer comprising at least two fractions of metal oxide particles different from each other in their average particle size and/or in the metal, and the electrode having active mass particles that are bonded together and to a current collector by an inorganic adhesive; and a process for their production.