Cable bacteria are long, multicellular micro-organisms that are capable of transporting electrons from cell to cell along the longitudinal axis of their centimeter-long filaments. The conductive structures that mediate this long-distance electron transport are thought to be located in the cell envelope. Therefore, this study examines in detail the architecture of the cell envelope of cable bacterium filaments through a combination of classical electron microscopy, cryo-based electron microscopy and tomography, focused ion beam-scanning electron microscopy and atomic force microscopy. We systematically imaged intact filaments with varying diameters. In addition, we investigated the periplasmic fiber sheath that remains after the cytoplasm and membranes have been removed by chemical extraction. Based on these investigations, we present a quantitative structural model of a cable bacterium. Cable bacteria build their cell envelope by a parallel concatenation of ridge compartments that have a standard size. Larger diameter filaments simply incorporate more parallel ridge compartments. Each ridge compartment contains a ~50 nm diameter fiber in the periplasmic space. These fibers are continuous across cell-to-cell junctions, which display a conspicuous cartwheel structure that is likely made by invaginations of the outer cell membrane around the periplasmic fibers. The continuity of the periplasmic fibers across cells makes them a prime candidate for the sought-after electron conducting structure in cable bacteria.