The discovery and repurposing of drugs require a deep understanding of the mechanism of drug action (MODA). Existing computational methods mainly model MODA with the protein-protein interaction (PPI) network. However, the molecular interactions of drugs in the human body are far beyond PPIs. Additionally, the lack of interpretability of these models hinders their practicability. We propose an interpretable deep learning-based path-reasoning framework (iDPath) for drug discovery and repurposing by capturing MODA on by far the most comprehensive multilayer biological network consisting of the complex high-dimensional molecular interactions between genes, proteins and chemicals. Experiments show that iDPath outperforms state-of-the-art machine learning methods on a general drug repurposing task. Further investigations demonstrate that iDPath can identify explicit critical paths that are consistent with clinical evidence. To demonstrate the practical value of iDPath, we apply it to the identification of potential drugs for treating prostate cancer and hypertension. Results show that iDPath can discover new FDA-approved drugs. This research provides a novel interpretable artificial intelligence perspective on drug discovery.