In human-robot interactions, human and robot agents maintain internal mental models of their environment, their shared task, and each other. The accuracy of these representations depends on each agent's ability to perform theory of mind, i.e. to understand the knowledge, preferences, and intentions of their teammate. When mental models diverge to the extent that it affects task execution, reconciliation becomes necessary to prevent the degradation of interaction. We propose a framework for bi-directional mental model reconciliation, leveraging large language models to facilitate alignment through semi-structured natural language dialogue. Our framework relaxes the assumption of prior model reconciliation work that either the human or robot agent begins with a correct model for the other agent to align to. Through our framework, both humans and robots are able to identify and communicate missing task-relevant context during interaction, iteratively progressing toward a shared mental model.