The prevalence of unhealthy eating habits has become an increasingly concerning issue in the United States. However, major food recommendation platforms (e.g., Yelp) continue to prioritize users' dietary preferences over the healthiness of their choices. Although efforts have been made to develop health-aware food recommendation systems, the personalization of such systems based on users' specific health conditions remains under-explored. In addition, few research focus on the interpretability of these systems, which hinders users from assessing the reliability of recommendations and impedes the practical deployment of these systems. In response to this gap, we first establish two large-scale personalized health-aware food recommendation benchmarks at the first attempt. We then develop a novel framework, Multi-Objective Personalized Interpretable Health-aware Food Recommendation System (MOPI-HFRS), which provides food recommendations by jointly optimizing the three objectives: user preference, personalized healthiness and nutritional diversity, along with an large language model (LLM)-enhanced reasoning module to promote healthy dietary knowledge through the interpretation of recommended results. Specifically, this holistic graph learning framework first utilizes two structure learning and a structure pooling modules to leverage both descriptive features and health data. Then it employs Pareto optimization to achieve designed multi-facet objectives. Finally, to further promote the healthy dietary knowledge and awareness, we exploit an LLM by utilizing knowledge-infusion, prompting the LLMs with knowledge obtained from the recommendation model for interpretation.