Depression is a serious mental illness that impacts the way people communicate, especially through their emotions, and, allegedly, the way they interact with others. This work examines depression signals in dialogs, a less studied setting that suffers from data sparsity. We hypothesize that depression and emotion can inform each other, and we propose to explore the influence of dialog structure through topic and dialog act prediction. We investigate a Multi-Task Learning (MTL) approach, where all tasks mentioned above are learned jointly with dialog-tailored hierarchical modeling. We experiment on the DAIC and DailyDialog corpora-both contain dialogs in English-and show important improvements over state-ofthe-art on depression detection (at best 70.6% F 1), which demonstrates the correlation of depression with emotion and dialog organization and the power of MTL to leverage information from different sources.