We study interacting bosons in a two-dimensional square bipartite optical lattice. By focusing on the regime where the first three excited bands are nearly degenerate (i.e., the first-excited p bands in one sublattice are nearly degenerate with the s band of the other sublattice), we derive a multi-orbital tight-binding model which captures the most relevant features of the band structure. 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.