In anticipation of the Gaia astrometric mission, a sample of spectroscopic binaries is being observed since 2010 with the Spectrograph pour l'Observation des PHenomenes des Interieurs stellaires et des Exoplanetes (SOPHIE) spectrograph at the Haute-Provence Observatory. Our aim is to derive the orbital elements of double-lined spectroscopic binaries (SB2s) with an accuracy sufficient to finally obtain the masses of the components with relative errors as small as 1 per cent when combined with Gaia astrometric measurements. In order to validate the masses derived from Gaia, interferometric observations are obtained for three SB2s in our sample with F-K components: HIP 14157, HIP 20601 and HIP 117186. The masses of the six stellar components are derived. Due to its edge-on orientation, HIP 14157 is probably an eclipsing binary. We note that almost all the derived masses are a few per cent larger than the expectations from the standard spectral type-mass calibration and mass-luminosity relation. Our calculation also leads to accurate parallaxes for the three binaries, and the Hipparcos parallaxes are confirmed.