Proteins with intrinsically disordered regions (IDRs) are common among eukaryotes. Many IDRs interact with nucleic acids and proteins. Annotation of these interactions is supported by computational predictors, but to date, only one tool that predicts interactions with nucleic acids was released, and recent assessments demonstrate that current predictors offer modest levels of accuracy. We have developed DeepDISOBind, an innovative deep multi-task architecture that accurately predicts deoxyribonucleic acid (DNA)-, ribonucleic acid (RNA)- and protein-binding IDRs from protein sequences. DeepDISOBind relies on an information-rich sequence profile that is processed by an innovative multi-task deep neural network, where subsequent layers are gradually specialized to predict interactions with specific partner types. The common input layer links to a layer that differentiates protein- and nucleic acid-binding, which further links to layers that discriminate between DNA and RNA interactions. Empirical tests show that this multi-task design provides statistically significant gains in predictive quality across the three partner types when compared to a single-task design and a representative selection of the existing methods that cover both disorder- and structure-trained tools. Analysis of the predictions on the human proteome reveals that DeepDISOBind predictions can be encoded into protein-level propensities that accurately predict DNA- and RNA-binding proteins and protein hubs. DeepDISOBind is available at https://www.csuligroup.com/DeepDISOBind/.