  We study interacting bosons in a two dimensional bipartite optical lattice.
By focusing on the regime where the first three excited bands are nearly
degenerate we derive a three orbital tight-binding model which captures the
most relevant features of the bandstructure. In addition, we also derive a
corresponding generalized Bose-Hubbard model and solve it numerically under
different situations, both with and without a confining trap. It is especially
found that the hybridization between sublattices can strongly influence the
phase diagrams and in a trap enable even appearances of condensed phases
intersecting the same Mott insulating plateaus.
