Ensemble learning aims to reduce the generalization error of the global model by reducing the bias and/or variance of the base models. Stacking is one such ensemble approach, which involves using a meta-model to aggregate the predictions of multiple base learners, often heterogeneous to increase diversity. The development of accurate algorithms for predicting medical insurance costs is essential for insurance companies to improve their productivity and efficiency. Ensemble methods appear as promising tools to provide robust and accurate predictions. In this article, we propose a multi-layer stacking model to predict the medical insurance costs. Additionally, two model-agnostic explanation techniques, Permutation Variable Importance (PVI) and SHapley Additive Explanations (SHAP), were implemented to detect and explain the factors influencing health insurance costs in the dataset. The results show that the stacking ensemble model outperforms all base models, namely K-nearest neighbors, Lasso regression, an SVM, random forests, and XGBoost, in terms of predictive performance. For the two XAI methods, although both produced similar results regarding the most important variables, the SHAP method is more sophisticated; in fact, it provides local and global interpretability in addition to indicating the direction of influence of each characteristic (positive or negative) on the predictions.