The intricacies of cancer present formidable challenges in achieving effective treatments. Despite extensive research in computational methods for drug response prediction, achieving personalized treatment insights remains challenging. Emerging solutions combine multiple omics data, leveraging graph neural networks to integrate molecular interactions into the reasoning process. However, effectively modeling and harnessing this information, as well as gaining the trust of clinical professionals remain complex. This paper introduces ExplainMIX, a pioneering approach that utilizes directed graph neural networks to predict drug responses with interpretability. ExplainMIX adeptly captures intricate structures and features within directed heterogeneous graphs, leveraging diverse data modalities such as genomics, proteomics, and metabolomics. ExplainMIX goes beyond prediction by generating transparent and interpretable explanations. Incorporating edge-level, metapath, and graph structure information, it provides meaningful insights into factors influencing drug response, supporting clinicians and researchers in the development of targeted therapies. Empirical results validate the efficacy of ExplainMIX in prediction and interpretation tasks by constructing a quantitative evaluation ground truth. This approach aims to contribute to precision medicine research by addressing challenges in interpretable personalized drug response prediction within the landscape of cancer. The dataset and source code of ExplainMIX are publicly available at https://github.com/AhauBioinformatics/ExplainMIX.