Robotic dexterous in-hand manipulation, where multiple fingers dynamically make and break contact, represents a step toward human-like dexterity in real-world robotic applications. Unlike learning-based approaches that rely on large-scale training or extensive data collection for each specific task, model-based methods offer an efficient alternative. Their online computing nature allows for ready application to new tasks without extensive retraining. However, due to the complexity of physical contacts, existing model-based methods encounter challenges in efficient online planning and handling modeling errors, which limit their practical applications. To advance the effectiveness and robustness of model-based contact-rich in-hand manipulation, this paper proposes a novel integrated framework that mitigates these limitations. The integration involves two key aspects: 1) integrated real-time planning and tracking achieved by a hierarchical structure; and 2) joint optimization of motions and contacts achieved by integrated motion-contact modeling. Specifically, at the high level, finger motion and contact force references are jointly generated using contact-implicit model predictive control. The high-level module facilitates real-time planning and disturbance recovery. At the low level, these integrated references are concurrently tracked using a hand force-motion model and actual tactile feedback. The low-level module compensates for modeling errors and enhances the robustness of manipulation. Extensive experiments demonstrate that our approach outperforms existing model-based methods in terms of accuracy, robustness, and real-time performance. Our method successfully completes five challenging tasks in real-world environments, even under appreciable external disturbances.