Uncertainties in dynamic road environments pose significant challenges for behavior and trajectory planning in autonomous driving. This paper introduces BoT-Drive, a planning algorithm that addresses uncertainties at both behavior and trajectory levels within a Partially Observable Markov Decision Process (POMDP) framework. BoT-Drive employs driver models to characterize unknown behavioral intentions and utilizes their model parameters to infer hidden driving styles. By also treating driver models as decision-making actions for the autonomous vehicle, BoT-Drive effectively tackles the exponential complexity inherent in POMDPs. To enhance safety and robustness, the planner further applies importance sampling to refine the driving trajectory conditioned on the planned high-level behavior. Evaluation on real-world data shows that BoT-Drive consistently outperforms both existing planning methods and learning-based methods in regular and complex urban driving scenes, demonstrating significant improvements in driving safety and reliability.