Artificial Intelligence models are increasingly used for classification tasks in healthcare. However, many healthcare professionals and machine learning engineers are still unaware of how these models contribute to and amplify biases. This work introduces a new framework (FAIR-MED) for bias detection and fairness evaluation in healthcare AI models, with a particular emphasis on intersectional fairness, which accounts for the compounded effects of multiple demographic attributes rather than assessing bias in isolation. Current methods often focus solely on data biases and overlook the compounded impact of multiple demographic attributes (e.g., age, gender, socioeconomic status) leading to unequal outcomes across diverse patient populations. To bridge this gap, a comprehensive, model-agnostic framework that incorporates a Compound Fairness Score is proposed. This approach to fairness goes beyond traditional methods by providing insights into the compounded impact of biases across different groups. Additionally, entropy-based weighting is introduced to quantify and aggregate bias metrics in a data-driven manner, ensuring that fairness evaluations prioritize the most impactful sources of bias. The proposed framework is evaluated on widely adopted families of AI models (linear, non-linear and neural network-based approaches) against open-source breast cancer dataset. The results suggest that Neural Networks may be more prone to amplifying existing biases, while Random Forest models tend to exhibit a better fairness balance in this evaluation. Logistic Regression, the most interpretable among the evaluated models, demonstrated overall stability but exhibited noticeable accuracy disparities across age groups. By aligning with transparency and accountability principles outlined in the EU AI Act, FAIR-MED offers a systematic, interpretable, and reproducible approach to bias analysis and fairness assessment, contributing to the development of ethical, equitable, and trustworthy AI-driven healthcare solutions.