This paper presents a unified prediction and planning algorithm for an autonomous vehicle to interact with an uncertain human-driven vehicle. Predicting human motion is challenging due to inherent uncertainties in diverse human internal states, i.e., driving styles and rationality. To address these complexities, we propose a hierarchical prediction strategy that combines data-driven internal state inference and planning-based human motion prediction. First, we employ Long Short Term Memory Networks (LSTM) based inference modules to capture both driving styles and rationality from the observed motion of human driver. With these inferred internal states, we predict the future trajectories of human-driven vehicle by formulating a human planning model as an optimization problem. Lastly, we present a Stochastic Model Predictive Control (SMPC) for the autonomous vehicle to safely interact with the human-driven vehicle while actively inferring human internal states. The simulation results, demonstrating the lane change scenarios, indicate the proposed method outperforms the existing work in both predicting the human motion and achieving the robot’s goal.