  We study mixtures of a population-imbalanced strongly-interacting Fermi gas
and of a Bose-Einstein condensed gas at zero temperature. In the homogeneous
case, we find that the Chandrasekhar-Clogston critical polarization for the
onset of instability of Fermi superfluidity is enhanced due to the interaction
with the bosons. Predictions for the critical polarization are also given in
the trapped case, with a special focus to the situation of equal Fermi-Bose and
Bose-Bose coupling constants, where the density of fermions becomes flat in the
center of the trap. This regime can be realized experimentally using Feshbach
resonances and is well suited to investigate the emergence of exotic
configurations, such as the occurrence of spin domains or the FFLO phase.
