Schizophrenia (SCZ) and depression (MDD) are two chronic mental disorders that seriously affect the quality of life of millions of people worldwide. We aim to develop machine-learning methods with objective linguistic, speech, facial, and motor behavioral cues to reliably predict the severity of psychopathology or cognitive function, and distinguish diagnosis groups. We collected and analyzed the speech, facial expressions, and body movement recordings of 228 participants (103 SCZ, 50 MDD, and 75 healthy controls) from two separate studies. We created an ensemble machine-learning pipeline and achieved a balanced accuracy of 75.3% for classifying the total score of negative symptoms, 75.6% for the composite score of cognitive deficits, and 73.6% for the total score of general psychiatric symptoms in the mixed sample containing all three diagnostic groups. The proposed system is also able to differentiate between MDD and SCZ with a balanced accuracy of 84.7% and differentiate patients with SCZ or MDD from healthy controls with a balanced accuracy of 82.3%. These results suggest that machine-learning models leveraging audio-visual characteristics can help diagnose, assess, and monitor patients with schizophrenia and depression.