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Aluminum nitride and silicon nitride have recently emerged as important nonlinear optical materials in integrated photonics for their quadratic and cubic optical nonlinearity, respectively. A composite aluminum nitride and silicon nitride waveguide structure, if realized, will simultaneously allow highly efficient second- and third-harmonic generation on the same chip platform and therefore assists 2f-3f self-referenced frequency combs. On-chip third-harmonic generation, being a higher-order nonlinear optics effect, is more demanding than second-harmonic generation due to the large frequency difference between the fundamental- and third-harmonic frequencies, which implies a large change of refractive indices and more stringent requirements on phase matching. In this work we demonstrate high-efficiency third-harmonic generation in a high-Q composite aluminum nitride/silicon nitride ring cavity. By carefully …