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Due to the advantage of achieving scalable connectivity and low-latency communications, air-ground integrated mesh networks (AGIMNs) will play an important role in the next generation wireless communication systems. However, due to the heterogeneous character of AGIMNs, it is challenging to manage the network and optimize the communication resources for improving the end-to-end (E2E) performance. Therefore, in this paper, we study a joint routing and time-frequency resource scheduling problem aiming at minimizing the total weighted E2E delay for heterogeneous AGIMNs. To capture the features of this complex system, we mathematically model the network constraints and formulate an optimization problem. To solve the original nonconvex problem, a suboptimal solution is proposed. First, we propose an optimal minimum-weight routing method, in which the hop count, conflict delay, and contention …