Model-based Offline Reinforcement Learning trains policies based on offline datasets and model dynamics, without direct real-world environment interactions. However, this method is inherently challenged by distribution shift. Previous approaches have primarily focused on tackling this issue directly leveraging off-policy mechanisms and heuristic uncertainty in model dynamics, but they resulted in inconsistent objectives and lacked a unified theoretical foundation. This paper offers a comprehensive analysis that disentangles the problem into two key components: model bias and policy shift. We provide both theoretical insights and empirical evidence to demonstrate how these factors lead to inaccuracies in value function estimation and impose implicit restrictions on policy learning. To address these challenges, we derive adjustment terms for model bias and policy shift within a unified probabilistic inference framework. These adjustments are seamlessly integrated into the vanilla reward function to create a novel Shifts-aware Reward (SAR), aiming at refining value learning and facilitating policy training. Furthermore, we introduce Shifts-aware Model-based Offline Reinforcement Learning (SAMBO-RL), a practical framework that efficiently trains classifiers to approximate the SAR for policy optimization. Empirically, we show that SAR effectively mitigates distribution shift, and SAMBO-RL demonstrates superior performance across various benchmarks, underscoring its practical effectiveness and validating our theoretical analysis.