We demonstrate on-chip, single-mode, waveguiding of light in air for a variety of 2D-3D photonic band gap (PBG) heterostructures. These include square spiral, woodpile, slanted pore, and inverse opal three-dimensional (3D) photonic crystals intercalated with a 2D (planar) photonic crystal microchip. Design rules are established to yield maximal single-mode waveguiding bandwidths of up to roughl...