A dual-wavelength digital holographic microscope to measure absolute volume of living cells is proposed. The optical setup allows us to reconstruct two quantitative phase contrast images at two different wavelengths from a single hologram acquisition. When adding the absorbing dye fast green FCF as a dispersive agent to the extracellular medium, cellular thickness can be univocally determined in the full field of view. In addition to the absolute cell volume, the method can be applied to derive important biophysical parameters of living cells including osmotic membrane water permeability coefficient and the integral intracellular refractive index (RI). Further, the RI of transmembrane flux can be determined giving an indication about the nature of transported solutes. The proposed method is applied to cultured human embryonic kidney cells, Chinese hamster ovary cells, human red blood cells, mouse cortical astrocytes, and neurons.