  We investigate an imbalanced mixture composed of two-color fermions and
scalar bosons in the hard-core limit, considering repulsive and attractive
interspecies and intraspecies interactions. The interplay between
commensurability, repulsive interactions and imbalance generates three
insulating phases: a mixed Mott state and two spin-selective insulators
characterized by the commensurability relations
$\rho_B+\rho^{\uparrow,(\downarrow)}_F=1$. For an attractive coupling between
fermions and bosons, we found the relations
$\rho_B-\rho^{\uparrow,(\downarrow)}_F=0$ for the spin-selective insulators.
State-of-the-art cold-atoms setups constitute ideal platforms to implement
these unveiled insulating states and verify their commensurability relations.
