We introduce DR-HAI -- a novel argumentation-based framework designed to extend model reconciliation approaches, commonly used in explainable AI planning, for enhanced human-AI interaction. By adopting a multi-shot reconciliation paradigm and not assuming a-priori knowledge of the human user's model, DR-HAI enables interactive reconciliation to address knowledge discrepancies between an explainer and an explainee. We formally describe the operational semantics of DR-HAI, provide theoretical guarantees related to termination and success, and empirically evaluate its efficacy. Our findings suggest that DR-HAI offers a promising direction for fostering effective human-AI interactions.