Quantitative Phase Imaging techniques such as DHM have emerged recently in life sciences and can be aimed at monitoring and quantifying non-invasively dynamic cellular processes modifying cell morphology and/or content. Concretely, the DHM phase signal depends on two cell parameters: cell thickness and integral refractive index. Consequently, due to its dual origin, the interpretation of the phase signal variations remain difficult. Since a net water flux across the cell membrane causes a variation of both parameters, the phase signal cannot be related directly to cellular RI or thickness variations, but must be understood as a coupled signal of these two parameters. We have developped a Dual-wavelength Digital Holographic Microscopy (DHM) setup to separately measure in a single shot fashion cellular thickness and integral RI of living cells. The method is based on the use of an absorbing dye that causes a high RI dispersion in the extracellular medium at the two recording wavelength. Consequently, the phase signals measured at the two wavelengths, differ significantly from each other. Practically, both cell RI and thickness can be univocally determined from the two phase measurements. Important biophysical parameters of living cells, including dry mass concentrations and water membrane permeability can be deduced.