State-of-the-art studies have demonstrated the superiority of joint modeling over pipeline implementation for medical named entity recognition and normalization due to the mutual benefits between the two processes. To exploit these benefits in a more sophisticated way, we propose a novel deep neural multi-task learning framework with explicit feedback strategies to jointly model recognition and normalization. On one hand, our method benefits from the general representations of both tasks provided by multi-task learning. On the other hand, our method successfully converts hierarchical tasks into a parallel multi-task setting while maintaining the mutual supports between tasks. Both of these aspects improve the model performance. Experimental results demonstrate that our method performs significantly better than state-of-theart approaches on two publicly available medical literature datasets.