Materials with negative compressibility can enable transformational technological advances spanning sensing, shielding, and optoelectronics. Virtually all materials exhibiting such expansion under pressure do so in one or two spatial directions, yet thermodynamics only forbid three-dimensional compression-induced expansion within the elastic regime absent of phase transitions. We show that a class of layered hybrid organic-inorganic metal oxides isolable through mild self-assembly reactions exhibits multiphase behavior under pressure, producing microscopic negative volume compressibility of their crystallographic unit cells. This phenomenon is only observed when molecular species bridge two-dimensional metal oxide layers. Chemical reduction─yielding mixed-valence hybrid bronzes─diminishes the effect. Evidence suggests that compression surmounts the boundary of elasticity via intermolecular carbon-carbon bond formation and structural distortion, driving interlayer expansion while liberating proton and electron equivalents.