Drug discovery is a challenging task, it takes several years for a drug to be introduced on the market, with most of the studied drugs not even passing the first phase. The understanding of the mechanisms influencing response to drugs can reduce failures and accelerate drug development. Virtual drug screening, based on Machine Learning models, is a promising field for the prediction of the outcome of a treatment. However, the complex relationships between the features learned by these models are still poorly understood and not easy to interpret. We have designed a Neural Network model for drug sensitivity prediction that leverages a Visible Neural Network, an easily interpretable model, due to its biologically informed nature. The trained model can be inspected to study which biological processes were fundamental for the prediction and to identify the drug properties that affect sensitivity. It combines multi-omics data from various types of tumor tissues and drug representations based on molecular descriptors. The mechanisms learned from the network can also be exploited to find candidate drugs for synergy to predict the effect of combined therapies. We consider the unbalanced nature of public drug screening datasets and show that our model outperforms state-of-the-art visible machine learning models.