  We analyze the possible types of ordering in a boson--fermion model. The
Hamiltonian is inherently related to the Bose--Hubbard model for vector
two-species bosons in optical lattices. We show that such model can be reduced
to the Kugel--Khomskii type spin--pseudospin model, but in contrast to the
usual version of the latter model, we are dealing here with the case of spin
$S=1$ and pseudospin $1/2$. We show that the interplay of spin and pseudospin
degrees of freedom leads to a rather nontrivial magnetic phase diagram
including the spin-nematic configurations. Tuning the spin-channel interaction
parameter $U_s$ gives rise to quantum phase transitions. We find that the
ground state of the system always has the pseudospin domain structure. On the
other hand, the sign change of $U_s$ switches the spin arrangement of the
ground state within domains from ferro- to aniferromagnetic one. Finally, we
revisit the spin (pseudospin)-1/2 Kugel--Khomskii model and see the inverse
picture of phase transitions.
