A solid-state three-dimensional battery assembly includes a solid bicontinuous monolithic carbon anode, a solid electrolyte layer, and a solid cathode. The solid monolithic carbon anode has an ordered three-dimensionally continuous network nanostructure, a length of at least 100 nm, and an average thickness of 3 to 90 nm. The ordered three-dimensionally continuous network nanostructure of the anode defines a plurality of pores having an average diameter of 5 to 100 nm. The solid electrolyte layer is disposed directly on the anode, has an average thickness of 3 to 90 nm, and fills a portion of the pores defined by the ordered three-dimensionally continuous network nanostructure of the anode. The solid cathode is disposed directly on the electrolyte layer, has an average thickness of 3 to 90 nm, and also fills a portion of the pores defined by the ordered three-dimensionally continuous network nanostructure of the anode. Related devices and methods are also provided.