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Depth estimation, visual odometry (VO), and bird's-eye-view (BEV) scene layout estimation present three critical tasks for driving scene perception, which is fundamental for motion planning and navigation in autonomous driving. Though they are complementary to each other, prior works usually focus on each individual task and rarely deal with all three tasks together. A naive way is to accomplish them independently in a sequential or parallel manner, but there are many drawbacks, i.e., 1) the depth and VO results suffer from the inherent scale ambiguity issue; 2) the BEV layout is directly predicted from the front-view image without using any depth-related information, although the depth map contains useful geometry clues for inferring scene layouts. In this paper, we address these issues by proposing a novel joint perception framework named JPerceiver, which can simultaneously estimate scale-aware depth and VO as well as BEV layout from a monocular video sequence. It exploits the cross-view geometric transformation (CGT) to propagate the absolute scale from the road layout to depth and VO based on a carefully-designed scale loss. Meanwhile, a cross-view and cross-modal transfer (CCT) module is devised to leverage the depth clues for reasoning road and vehicle layout through an attention mechanism. JPerceiver can be trained in an end-to-end multi-task learning way, where the CGT scale loss and CCT module promote inter-task knowledge transfer to benefit feature learning of each task. Experiments on Argoverse, Nuscenes and KITTI show the superiority of JPerceiver over existing methods on all the above three tasks in terms of accuracy, model size, and inference speed. The code and models are available at~\href{https://github.com/sunnyHelen/JPerceiver}{https://github.com/sunnyHelen/JPerceiver}.