Multispectral tissue imaging based on optical cameras and continuous-wave tissue illumination is commonly used in medicine and biology. Surprisingly, there is a characteristic absence of a critical look at the quantities that can be uniquely characterized from optically diffuse matter by multispectral imaging. Here, we investigate the fundamental question of uniqueness in epi-illumination measurements from turbid media obtained at multiple wavelengths. By utilizing an analytical model, tissue-mimicking phantoms, and an in vivo imaging experiment we show that independent of the bands employed, spectral measurements cannot uniquely retrieve absorption and scattering coefficients. We also establish that it is, nevertheless, possible to uniquely quantify oxygen saturation and the Mie scattering power-a previously undocumented uniqueness condition.