By allowing a large number of links to be simultaneously transmitted, directional antenna arrays with beamforming have been envisioned as a promising candidate to reach unprecedented levels of spatial isolation. To achieve the high efficiency of spatial reuse in improving system performance, an optimization problem that maximizes the achievable data rate of a multihop heterogeneous network, which incorporates the concept of integrated access and backhaul and supports both downlink and uplink transmissions on access and backhaul links, is formulated. The optimization problem is then systematically decomposed and demonstrated as NP-hard, and a heuristic joint scheduling and resource allocation algorithm is proposed to maximize the achievable data rate. In addition, an efficient dynamic routing algorithm is proposed to further enhance the data rate. With extensive system-level simulations, it is demonstrated that the proposed algorithms achieve significant gain over benchmark schemes, in terms of data rate, and closely approach the theoretical optimum, yet with lower latency. Besides, the proposed algorithms enable a flexible adjustment of downlink and uplink transmission duration allocation and support both half- and full-duplex modes with considerable performance enhancement. In particular, the proposed algorithms are capable of fulfilling different performance requirements for both point-to-point and point-to-multipoint communications.