The materials that are used to make electrodes and their internal structures significantly affect microbial fuel cell (MFC) performance. In this study, we describe a carbon nanotube (CNT)–sponge composite prepared by coating a sponge with CNTs. Compared to the CNT-coated textile electrodes evaluated in prior studies, CNT–sponge electrodes had lower internal resistance, greater stability, more tunable and uniform macroporous structure (pores up to 1 mm in diameter), and improved mechanical properties. The CNT–sponge composite also provided a three-dimensional scaffold that was favorable for microbial colonization and catalytic decoration. Using a batch-fed H-shaped MFC outfitted with CNT–sponge electrodes, an areal power density of 1.24 W m−2 was achieved when treating domestic wastewater. The maximum volumetric power density of a continuously fed plate-shaped MFC was 182 W m−3. To our knowledge, these are the highest values obtained to date for MFCs fed domestic wastewater: 2.5 times the previously reported maximum areal power density and 12 times the previously reported maximum volumetric power density.