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(Abridged) Differential astrometry measurements from the PalomarHigh-precision Astrometric Search for Exoplanet Systems (PHASES) are used toconstrain the astrometric orbit of the previously known lesssim 2 day subsystemin the triple system 63 Gem A and have detected a previously unknown 2 yearKeplerian wobble superimposed on the visual orbit of the much longer period(213 years) binary system HR 2896. The very small astrometric perturbationcaused by the inner pair in 63 Gem A stretches the limits of currentastrometric capabilities, but PHASES observations are able to constrain theorientation of the orbit. The two bright stars comprising the HR 2896 longperiod (213 year) system have a combined spectral type of K0III and the newlydetected object's mass estimate places it in the regime of being a M dwarf. Themotion of the stars are slow enough that their spectral features are alwaysblended, preventing Doppler studies. The PHASES measurements and radialvelocities (when available) have been combined with lower precisionsingle-aperture measurements covering a much longer timeframe to improve thecharacterization of the long period orbits in both binaries. The visual orbitsof the short and long period systems are presented for both systems, and usedto calculate two possible values of the mutual inclinations between inner andouter orbits of 152 pm 12 degrees or a less likely value of 31 pm 11 degreesfor 63 Gem A and 10.2 pm 2.4 degrees or 171.2 pm 2.8 degrees for HR 2896. Thefirst is not coplanar, whereas the second is either nearly coplanar oranti-coplanar.

The PHASES Differential Astrometry Data Archive IV: The Triple Star Systems 63 Gem A and HR 2896