  Superfluid-insulator transitions in a one-dimensional mixture of two-color
fermions and scalar bosons are studied within the framework of the
Bose-Fermi-Hubbard model. Zero-temperature phase diagrams are constructed for
repulsive intraspecies interactions and attractive or repulsive interspecies
couplings. In addition to the trivial Mott insulator phases, we report the
emergence of new non-trivial insulator phases that depend on the sign of the
boson-fermion interaction. These non-trivial insulator phases satisfy the
conditions $\rho_B\pm\rho_F=n$ and $\rho_B\pm \tfrac{1}{2}\rho_F=n$, with the
plus (minus) sign for repulsive (attractive) interactions and $n$ an integer.
Far from fermionic half-filling, the boson-fermion interaction drives a
gapless-gapped transition in the spin sector. Our findings could be observed
experimentally in state-of-the-art cold-atom setups.
