Modeling and understanding spatiotemporal graphs have been a long-standing research topic in network science and typically replies on network processing hypothesized by human knowledge. In this paper, we aim at pushing forward the modeling and understanding of spatiotemporal graphs via new disentangled deep generative models. Specifically, a new Bayesian model is proposed that factorizes spatiotemporal graphs into spatial, temporal, and graph factors as well as the factors that explain the interplay among them. A variational objective function and new mutual information thresholding algorithms driven by information bottleneck theory have been proposed to maximize the disentanglement among the factors with theoretical guarantees. Qualitative and quantitative experiments on both synthetic and real-world datasets demonstrate the superiority of the proposed model over the state-of-the-art by up to 69.2\% for graph generation and 41.5\% for interpretability.