In this paper, we present an Adaptive Multimodal Dialogue System for Depressive and Anxiety Disorders Screening (DADS). The system interacts with the user through verbal and non-verbal communication to elicit the information needed to make referrals and recommendations for depressive and anxiety disorders while encouraging the user and keeping them calm. We designed the problem using interconnected Markov Decision Processes using sub-goals to deal with the large state space. We present the problem formulation and the experimental procedure for the training data collection and the system training following the methodology of Wizard-of-Oz experiments. Keywords Multimodal Adaptive Dialogue Systems, Markov Decision Processes, Reinforcement Learning, Mental Health Monitoring, Wizard-of-Oz