  We study a gas of dipolar Bosons confined in a two-dimensional optical
lattice. Dipoles are considered to point freely in both up and down directions
perpendicular to the lattice plane. This results in a nearest neighbor
repulsive (attractive) interaction for aligned (anti-aligned) dipoles. We find
regions of parameters where the ground state of the system exhibits insulating
phases with ferromagnetic or anti-ferromagnetic ordering, as well as with
rational values of the average magnetization. Evidence for the existence of a
novel counterflow supersolid quantum phase is also presented.
