Drug discovery is a challenging task, characterized by a protracted period of time between initial development and market release, with a high rate of attrition at each stage. Computational virtual screening, powered by machine learning algorithms, has emerged as a promising approach for predicting therapeutic efficacy. However, the complex relationships between features learned by these algorithms can be challenging to decipher. We have devised a neural network model for the prediction of drug sensitivity, which employs a biologically-informed visible neural network (VNN), enabling a greater level of interpretability. The trained model can be scrutinized to investigate the biological pathways that play a fundamental role in prediction, as well as the chemical properties of drugs that influence sensitivity. The model leverages multi-omics data obtained from diverse tumor tissue sources and molecular descriptors that encode drug properties. We have extended the model to predict drug synergy, resulting in favorable outcomes while retaining interpretability. Given the often imbalanced nature of publicly available drug screening datasets, our model demonstrates superior performance compared to state-of-the-art visible machine learning algorithms.