Drug-drug interactions (DDIs) and drug-disease interactions (DDXs) are critical issues for the healthcare system and clinical physicians. Typical statistical approaches, such as generalized linear models, cannot systematically handle the complexity of DDIs and DDXs. Although deep neural networks can predict DDIs and DDXs with high accuracy, they often require large numbers of training data, and how such black-box models arrive at predictions is still not well understood. Therefore, we propose a novel interpretable representation learning algorithm, Deep Rule Forest (DRF) to help discover rules from multi-layer tree-based models as the combinations of drug usages and disease indications to help identify DDIs and DDXs. In this paper, we introduce a real-world application of our approach to acute kidney injury (AKI), which is a typical unfavorable outcome that could be triggered by DDIs/DDXs. The sample data were obtained from a population of one million individuals randomly selected from the Taiwan National Health Insurance Database. The experimental result shows that the combinations of several diseases and drug prescriptions are associated with AKI. Also, the DRF combined with other machine learning algorithms perform comparatively higher than typical tree/rule-based and other state-of-the-art algorithms in terms of accuracy of prediction and model interpretability.