We report the X-ray solid state structures of two tertiary squaramides, i.e. 3-(diethylamino)-4-ethoxy-cyclobutene-1,2-dione (1) and bis-3,4-(diethylamino)-cyclobutene-1,2-dione (2). Compound 1 forms electrostatically compressed dimers in the solid state. Moreover, compound 2 exhibits a remarkable solid state architecture resembling a lipid bilayer. This supramolecular assembly has been analyzed using high level DFT calculations and Bader's theory of "atoms-in-molecules". The antiparallel CO⋯CO interactions of the cyclobutenedione rings and hydrophobic interactions involving the ethyl chains are crucial for the formation of the bilayer assembly in the solid state