  We discuss the interband light tunneling in a two-dimensional periodic
photonic structure, as was studied recently in experiments for
optically-induced photonic lattices [H. Trompeter et al., Phys. Rev. Lett.
\textbf{96}, 053903 (2006)]. We identify the Zener tunneling regime at the
crossing of two Bloch bands, which occurs in a generic case of the Bragg
reflection when the Bloch index crosses the edge of the irreducible Brillouin
zone. Similarly, the higher-order Zener tunneling involves four Bloch bands
when the Bloch index passes through a high-symmetry point on the edge of the
Brillouin zone. We derive simple analytical models that describe the tunneling
effect, and calculate the corresponding tunneling probabilities.
