With more than 300 million people depressed worldwide, depression is a global problem. Due to access barriers such as social stigma, cost, and treatment availability, 60% of mentally-ill adults do not receive any mental health services. Effective and efficient diagnosis relies on detecting clinical symptoms of depression. Automatic detection of depressive symptoms would potentially improve diagnostic accuracy and availability, leading to faster intervention. In this work, we present a machine learning method for measuring the severity of depressive symptoms. Our multi-modal method uses 3D facial expressions and spoken language, commonly available from modern cell phones. It demonstrates an average error of 3.67 points (15.3% relative) on the clinically-validated Patient Health Questionnaire (PHQ) scale. For detecting major depressive disorder, our model demonstrates 83.3% sensitivity and 82.6% specificity. Overall, this paper shows how speech recognition, computer vision, and natural language processing can be combined to assist mental health patients and practitioners. This technology could be deployed to cell phones worldwide and facilitate low-cost universal access to mental health care.