Biological single-cell sequencing data can be used to learn about cellular phenotypes, developmental trajectories, and disease. It is increasingly utilized to measure a cell's molecular state across perturbations. To better understand a cellular system, we develop a machine learning model that can accurately predict drug-induced perturbations in multiomic single-cell readouts. We focus on an interpretable deep-learning approach applicable to a wide range of cell-types and perturbations. Such a generic model facilitates the design of optimal treatments, and can be used to generate and validate hypotheses about underlying biological processes.