In human-AI collaboration, a central challenge is deciding whether the AI should handle a task, be deferred to a human expert, or be addressed through collaborative effort. Existing Learning to Defer approaches typically make binary choices between AI and humans, neglecting their complementary strengths. They also lack interpretability, a critical property in high-stakes scenarios where users must understand and, if necessary, correct the model's reasoning. To overcome these limitations, we propose Defer-and-Complement Decision-Making via Decoupled Concept Bottleneck Models (DeCoDe), a concept-driven framework for human-AI collaboration. DeCoDe makes strategy decisions based on human-interpretable concept representations, enhancing transparency throughout the decision process. It supports three flexible modes: autonomous AI prediction, deferral to humans, and human-AI collaborative complementarity, selected via a gating network that takes concept-level inputs and is trained using a novel surrogate loss that balances accuracy and human effort. This approach enables instance-specific, interpretable, and adaptive human-AI collaboration. Experiments on real-world datasets demonstrate that DeCoDe significantly outperforms AI-only, human-only, and traditional deferral baselines, while maintaining strong robustness and interpretability even under noisy expert annotations.