A suspension of nanoparticles with very low volume fraction is found to assemble into a macroscopic cellular phase that is composed of particle-rich walls and particle-free voids under the collective influence of AC and DC voltages. Systematic study of this phase transition shows that it was the result of electrophoretic assembly into a two-dimensional configuration followed by spinodal decomposition into particle-rich walls and particle-poor cells mediated principally by electrohydrodynamic flow. This mechanistic understanding reveals two characteristics needed for a cellular phase to form, namely (1) a system that is considered two dimensional and (2) short-range attractive, long-range repulsive interparticle interactions. In addition to determining the mechanism underpinning the formation of the cellular phase, this work presents a method to reversibly assemble microscale continuous structures out of nanoscale particles in a manner that may enable the creation of materials that impact diverse fields including energy storage and filtration.