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Globally interpretable models are a promising approach for trustworthy AI in safety-critical domains. Alongside global explanations, detailed local explanations are a crucial complement to effectively support human experts during inference. This work proposes the Calibrated Hierarchical QPM (CHiQPM) which offers uniquely comprehensive global and local interpretability, paving the way for human-AI complementarity. CHiQPM achieves superior global interpretability by contrastively explaining the majority of classes and offers novel hierarchical explanations that are more similar to how humans reason and can be traversed to offer a built-in interpretable Conformal prediction (CP) method. Our comprehensive evaluation shows that CHiQPM achieves state-of-the-art accuracy as a point predictor, maintaining 99% accuracy of non-interpretable models. This demonstrates a substantial improvement, where interpretability is incorporated without sacrificing overall accuracy. Furthermore, its calibrated set prediction is competitively efficient to other CP methods, while providing interpretable predictions of coherent sets along its hierarchical explanation.