To reach energy density demands greater than 3 mA h cm-2 for practical applications, the electrode structure of lithium-sulfur batteries must undergo an architectural redesign. Freestanding carbon nanofoam papers derived from resorcinol-formaldehyde aerogels provide a three-dimensional conductive mesoporous network while facilitating electrolyte transport. Vapor-phase sulfur infiltration fully penetrates >100 μm thick electrodes and conformally coats the carbon aerogel surface providing areal capacities up to 4.1 mA h cm-2 at sulfur loadings of 6.4 mg cm-2. Electrode performance can be optimized for energy density or power density by tuning sulfur loading, pore size, and electrode thickness.