  We aim at detecting and characterizing the main-sequence companions of a
sample of known and suspected Galactic binary Cepheids. We used the
multi-telescope interferometric combiners MIRC and PIONIER to detect and
measure the astrometric positions of the high-contrast companions orbiting 16
bright Galactic Cepheids. We made use of the CANDID algorithm to search for the
companions and set detection limits. We also present new high-precision RVs
which were used to fit radial pulsation and orbital velocities. We report the
detection of the companions orbiting the Cepheids U Aql, BP Cir, and S Mus,
possible detections for FF Aql, Y Car, BG Cru, X Sgr, V350 Sgr, and V636 Sco,
while no component is detected around U Car, YZ Car, T Mon, R Mus, S Nor, W Sgr
and AH Vel. For U Aql and S Mus, we performed a preliminary orbital fit
combining astrometry with new high-precision RVs, providing the full set of
orbital and pulsation parameters. Assuming the distance, we estimated
preliminary masses of M(U Aql) = 4.97+/-0.62Msun and M(S Mus) =
4.63+/-0.99Msun. For YZ Car, W Sgr, V350 Sgr, and V636 Sco, we revised the
spectroscopic orbits using new high-precision RVs, while we updated the
pulsation parameters for BP Cir, BG Cru, S Nor and AH Vel. Our interferometric
observations also provide measurements of the angular diameters, that can be
used in a Baade-Wesselink type analysis. We have now several astrometric
detections of Cepheid companions. When RVs of the companions will be available,
such systems will provide accurate and independent masses and distances.
Orbital parallaxes with an accuracy <5% will be particularly useful for a
better calibration of the P-L relation. The final Gaia parallaxes will be also
particularly helpful for single-line spectroscopic systems, where mass and
distance are degenerate. Mass measurements are necessary for a better
understanding of the age and evolution of Cepheids
