Mental distress like depression and anxiety contribute to the largest proportion of the global burden of diseases. Automated diagnosis system of such disorders, empowered by recent innovations in Artificial Intelligence, can pave the way to reduce the sufferings of the affected individuals. Development of such systems requires information-rich and balanced corpora. In this work, we introduce a novel mental distress analysis audio dataset DEPAC, labelled based on established thresholds on depression and anxiety standard screening tools. This large dataset comprises multiple speech tasks per individual, as well as relevant demographic information. Alongside, we present a feature set consisting of hand-curated acoustic and linguistic features, which were found effective in identifying signs of mental illnesses in human speech. Finally, we justify the quality and effectiveness of our proposed audio corpus and feature set in predicting depression severity by comparing the performance of baseline machine learning models built on this dataset with baseline models trained on other well-known depression corpora.