In multiradio multichannel (MR-MC) networks with significantly expanded network resource space, many existing scheduling/routing algorithms rely on a link-based network model and apply different heuristics in algorithm design to achieve/approximate throughput optimality. In this paper, using a tuple-based multidimensional conflict graph model, we establish a cross-layer framework, which facilitates systematically studying distributed scheduling and routing in multihop multipath MR-MC networks. In this framework, each tuple link is installed with a routing controller, which feeds controlled amounts of data to the tuple-link output queues for scheduling and transmission. We rigorously prove that, under a set of certain conditions, the network is queue stable in the mean sense under the distributed maximal scheduling policy. Based on Lyapunov optimization, we further propose a distributed delay-aware multipath routing method, which aims at minimizing the end-to-end delay of each commodity flow. Extensive simulation results demonstrate that the proposed joint scheduling/routing algorithm outperforms existing link-based single-path and multipath algorithms and tuple-based cross-layer control algorithm.