Context. Orbital motion in binary and planetary systems is the main source of precise stellar and planetary mass measurements, and the joint analysis of data obtained using multiple observational methods can both lift degeneracies and improve precision. Aims. We set out to measure the masses of individual stars in binary systems using all the information brought by the H IPPARCOS and Gaia absolute astrometric missions. Methods. We present BINARYS, a tool that uses the H IPPARCOS and Gaia absolute astrometric data and combines them with relative astrometry and/or radial velocity measurements to determine the orbit of a binary system. This tool rigorously combines the H IPPARCOS and Gaia data (here EDR3) and can use the H IPPARCOS Transit Data as needed for binaries where H IPPARCOS detects significant flux from the secondary component. It also supports the case where Gaia has resolved the system, giving an astrometric solution for both components. Results. We determine model-independent individual masses for the first time for three systems: the two mature binaries Gl 494 ( M1 = 0.584 ± 0.003 M⊙ and M2 = 87 ± 1 MJup) and HIP 88745 ( M1 = 0.96 ± 0.02 M⊙ and 0.62 -0.008+0.009 ), and the younger AB Dor member GJ 2060 (1926 -6+7 and 0.882 -0.005+0.004). The latter provides a rare test of evolutionary model predictions at young ages in the low-stellar-mass range and sets a lower age limit of 100 Myr for the moving group.