Disease causing pathogens such as viruses, introduce their proteins into the host cells where they interact with the host’s proteins enabling the virus to replicate inside the host. These interactions between pathogen and host proteins are key to understanding infectious diseases. Often multiple diseases involve phylogenetically related or biologically similar pathogens. Here we present a multitask learning method to jointly model interactions between human proteins and three different, but related viruses: Hepatitis C, Ebola virus and Influenza A. Our multitask matrix completion based model uses a shared low-rank structure in addition to a task-specific sparse structure to incorporate the various interactions. We obtain upto a 39% improvement in predictive performance over prior state-of-the-art models.We show how our model’s parameters can be interpreted to reveal both general and specific interactionrelevant characteristics of the viruses. Our code, data and supplement is available at: http://www.cs.cmu.edu/∼mkshirsa/bsl mtl.