We propose the molecular omics network (MOOMIN) a multimodal graph neural network used by AstraZeneca oncologists to predict the synergy of drug combinations for cancer treatment. Our model learns drug representations at multiple scales based on a drug-protein interaction network and metadata. Structural properties of compounds and proteins are encoded to create vertex features for a message-passing scheme that operates on the bipartite interaction graph. Propagated messages form multi-resolution drug representations which we utilized to create drug pair descriptors. By conditioning the drug combination representations on the cancer cell type we define a synergy scoring function that can inductively score unseen pairs of drugs. Experimental results on the synergy scoring task demonstrate that MOOMIN outperforms state-of-the-art graph fingerprinting, proximity preserving node embedding, and existing deep learning approaches. Further results establish that the predictive performance of our model is robust to hyperparameter changes. We demonstrate that the model makes high-quality predictions over a wide range of cancer cell line tissues, out-of-sample predictions can be validated with external synergy databases, and that the proposed model is data efficient at learning.