Quantitative measurements of physical parameters become increasingly important for understanding biological processes. Brillouin microscopy (BM) has recently emerged as one technique providing the 3D distribution of viscoelastic properties inside biological samples — so far relying on the implicit assumption that refractive index (RI) and density can be neglected. Here, we present a novel method (FOB microscopy) combining BM with optical diffraction tomography and epi-fluorescence imaging for explicitly measuring the Brillouin shift, RI and absolute density with specificity to fluorescently labeled structures. We show that neglecting the RI and density might lead to erroneous conclusions. Investigating the nucleoplasm of wild-type HeLa cells, we find that it has lower density but higher longitudinal modulus than the cytoplasm. Thus, the longitudinal modulus is not merely sensitive to the water content of the sample — a postulate vividly discussed in the field. We demonstrate the further utility of FOB on various biological systems including adipocytes and intracellular membraneless compartments. FOB microscopy can provide unexpected scientific discoveries and shed quantitative light on processes such as phase separation and transition inside living cells.