The integration of machine learning (ML) into healthcare demands rigorous fairness assurance to prevent algorithmic biases from exacerbating disparities in treatment. This study introduces FairHealthGrid, a systematic framework for evaluating bias mitigation strategies across healthcare ML models. Our framework combines grid search with a composite fairness score, incorporating fairness metrics weighted by risk tolerances. As output, we present a trade-off map concurrently evaluating accuracy and fairness, categorizing solutions (model + bias mitigation) into the following regions: Win-Win, Good, Poor, Inverted, or Lose-Lose. We apply the framework on three different healthcare datasets. Results reveal significant variability across different healthcare applications. The framework identifies model-bias mitigation for balancing equity and accuracy, yet highlights the absence of universal solutions. By enabling systematic trade-off analysis, FairHealthGrid allows healthcare stakeholders to audit, compare, and select ethically aligned ML models for specific healthcare applications—advancing towards equitable AI in healthcare.