Simultaneous distance measurements on two or more optical wavelengths enable dispersion-based correction of deviations that result from insufficient knowledge of the refractive index along the signal propagation path. We demonstrate a supercontinuum-based approach for highly accurate distance measurements suitable for such an inline refractivity compensation. The distance is estimated from the phase delay observations on the intermode beats. We use a supercontinuum (SC) coherently broadened from a 780 nm frequency comb and spanning the spectral range of 570-970 nm. Experiments are performed on the 590 and 890 nm wavelength bands filtered from the SC spectrum. Results show distance measurements with standard deviations of around 0.01 mm at 50 m, and a distance-dependent component below 0.2 ppm on the individual spectral bands. Distance residuals compared to a reference interferometer are on the order of 0.1 ppm for displacements up to 50 m. Controlled pressure-induced refractivity variations are created over a length of 15 m, resulting in an optical path length change of 0.4 mm. Using the two-color method, we demonstrate refractivity-corrected distance measurement with a standard deviation of around 0.08 mm for a 60 s averaging window. The current experimental configuration can be easily extended to distance measurements on more than two wavelengths. The results highlight its potential for practical long-distance measurements through inline refractivity compensation.