III-Nitride semiconductors offer a versatile platform for integrated photonic circuits operating from the ultraviolet to the near-infrared spectral range. Either pure AlN or pure GaN waveguiding layers have usually been investigated so far. In this work, we report on the study of GaN/AlN bilayers epitaxially-grown on a sapphire substrate for photonic circuits. Quality factors up to 410,000 are demonstrated with microring resonators in the near-infrared spectral range. We emphasize the peculiar advantages of these bilayers for nonlinear photonics: GaN offers a larger nonlinear susceptibility as compared to AlN. More importantly, both materials exhibit nonlinear susceptibilities with opposite signs that can be advantageous for nonlinear conversion. Thick epitaxial III-nitride bilayers are associated with the occurrence of cracks in the epi-layers and multimode waveguide propagation. We show that the multimode character can lead to peculiar resonance line shapes with the capacity to control full transmission and reflection by phase engineering.