Decision and control are core functionalities of high-level automated vehicles. Current mainstream methods, such as functionality decomposition and end-to-end reinforcement learning (RL), either suffer high time complexity or poor interpretability and adaptability on real-world autonomous driving tasks. In this paper, we present an interpretable and computationally efficient framework called integrated decision and control (IDC) for automated vehicles, which decomposes the driving task into static path planning and dynamic optimal tracking that are structured hierarchically. First, the static path planning generates several candidate paths only considering static traffic elements. Then, the dynamic optimal tracking is designed to track the optimal path while considering the dynamic obstacles. To that end, we formulate a constrained optimal control problem (OCP) for each candidate path, optimize them separately and follow the one with the best tracking performance. To unload the heavy online computation, we propose a model-based reinforcement learning (RL) algorithm that can be served as an approximate constrained OCP solver. Specifically, the OCPs for all paths are considered together to construct a single complete RL problem and then solved offline in the form of value and policy networks, for real-time online path selecting and tracking respectively. We verify our framework in both simulations and the real world. Results show that compared with baseline methods IDC has an order of magnitude higher online computing efficiency, as well as better driving performance including traffic efficiency and safety. In addition, it yields great interpretability and adaptability among different driving tasks. The effectiveness of the proposed method is also demonstrated in real road tests with complicated traffic conditions.