An adverse drug event (ADE) is an injury resulting from medical intervention related to a drug. Automatic ADE detection from text is either fine-grained (ADE entity recognition) or coarse-grained (ADE assertive sentence classification), with limited efforts leveraging inter-dependencies among the two granularities. We instead propose a multi-grained joint deep network to concurrently learn the ADE entity recognition and ADE sentence classification tasks. Our joint approach takes advantage of their symbiotic relationship, with a transfer of knowledge between the two levels of granularity. Our dual-attention mechanism constructs multiple distinct representations of a sentence that capture both task-specific and semantic information in the sentence, providing stronger emphasis on the key elements essential for sentence classification. Our model improves state-of- art F1-score for both tasks: (i) entity recognition of ADE words (12.5% increase) and (ii) ADE sentence classification (13.6% increase) on MADE 1.0 benchmark of EHR notes.