We suggest a new multimodal imaging technique for quantitatively measuring the integral (thickness-average) refractive index of the nuclei of live biological cells in suspension. For this aim, we combined quantitative phase microscopy with simultaneous 2-D fluorescence microscopy. We used 2-D fluorescence microscopy to localize the nucleus inside the quantitative phase map of the cell, as well as for measuring the nucleus radii. As verified offline by both 3-D confocal fluorescence microscopy and 2-D fluorescence microscopy while rotating the cells during flow, the nucleus of cells in suspension that are not during division can be assumed to be an ellipsoid. The entire shape of a cell in suspension can be assumed to be a sphere. Then, the cell and nucleus 3-D shapes can be evaluated based on their in-plain radii available from the 2-D phase and fluorescent measurements, respectively. Finally, the nucleus integral refractive index profile is calculated. We demonstrate the new technique on cancer cells, obtaining nucleus refractive index values that are lower than those of the cytoplasm, coinciding with recent findings. We believe that the proposed technique has the potential to be used for flow cytometry, where full 3-D refractive index tomography is too slow to be implemented during flow.