Explainable machine learning (XML) has emerged as a major challenge in artificial intelligence (AI). Although black-box models such as Deep Neural Networks and Gradient Boosting often exhibit exceptional predictive accuracy, their lack of interpretability is a notable drawback, particularly in domains requiring transparency and trust. This paper tackles this core AI problem by proposing a novel method to enhance explainability with minimal accuracy loss, using a Mixture of Linear Models (MLM) estimated under the co-supervision of black-box models. We have developed novel methods for estimating MLM by leveraging AI techniques. Specifically, we explore two approaches for partitioning the input space: agglomerative clustering and decision trees. The agglomerative clustering approach provides greater flexibility in model construction, while the decision tree approach further enhances explainability, yielding a decision tree model with linear or logistic regression models at its leaf nodes. Comparative analyses with widely-used and state-of-the-art predictive models demonstrate the effectiveness of our proposed methods. Experimental results show that statistical models can significantly enhance the explainability of AI, thereby broadening their potential for real-world applications. Our findings highlight the critical role that statistical methodologies can play in advancing explainable AI.