Cutting-edge connected vehicle (CV) technologies have drawn much attention in recent years. The real-time traffic data captured by a CV can be shared with other CVs and data centers so as to open new possibilities for solving diverse transportation problems. However, imagery captured by onboard cameras in a connected environment, are not sufficiently investigated, especially for safety and health-oriented visual perception. In this paper, a bidirectional process of image synthesis and decomposition (BPISD) approach is proposed, and thus a novel self-supervised multi-task learning framework, to simultaneously estimate depth map, atmospheric visibility, airlight, and PM2.5 mass concentration, in which depth map and visibility are considered highly associated with traffic safety, while airlight and PM2.5 mass concentration are directly correlated with human health. Both the training and testing phases of the proposed system solely require a single image as input. Due to the innovative training pipeline, the depth estimation network can manage various levels of visibility conditions and overcome inherent problems in current image-synthesis-based depth estimation, thereby generating high-quality depth maps even in low-visibility situations and further benefiting accurate estimations of visibility, airlight, and PM2.5 mass concentration. Extensive experiments on the synthesized data from the KITTI and real-world data collected in Beijing demonstrate that the proposed method can (1) achieve performance competitive in depth estimation as compared with state-of-the-art methods when taking clear images as input; (2) predict vivid depth map for images contaminated by various levels of haze; and (3) accurately estimate visibility, airlight, and PM2.5 mass concentrations. Beneficial applications can be developed based on the presented work to improve traffic safety, air quality, and public health.