The prevalence of unhealthy eating habits has become a growing concern in the United States. However, popular food recommendation platforms, such as Yelp, tend to prioritize users' dietary preferences over the healthiness of their choices. While some efforts have focused on developing health-aware food recommendation systems, personalization based on specific health conditions remains underexplored. Additionally, the lack of interpretability in these systems prevents users from evaluating the reliability of recommendations, limiting their practical adoption. To address these issues, we introduce two large-scale personalized health-aware food recommendation benchmarks at the first attempt. Building on this, we propose a novel framework called the Multi-Objective Personalized Interpretable Health-aware Food Recommendation System (MOPI-HFRS). This system generates food recommendations by jointly optimizing three objectives: user preference, personalized healthiness, and nutritional diversity. It also incorporates a reasoning module enhanced by large language models (LLMs) to provide interpretable recommendations that promote healthy dietary knowledge. The framework integrates descriptive features and health data using two structure learning and pooling modules within a graph learning framework. Pareto optimization is applied to balance the multi-faceted objectives. To further enhance healthy dietary knowledge, the system leverages LLMs by infusing knowledge from the recommendation model, generating meaningful interpretations for the recommendations. Extensive experiments on the proposed benchmarks demonstrate that MOPI-HFRS outperforms state-of-the-art methods by delivering diverse, healthy food recommendations alongside reliable explanations.