Traditional applications of natural language processing (NLP) in healthcare have predominantly focused on patient-centered services, enhancing patient interactions and care delivery, such as through medical dialogue systems. However, the potential of NLP to benefit inexperienced doctors, particularly in areas such as communicative medical coaching, remains largely unexplored. We introduce ``ChatCoach,'' an integrated human-AI cooperative framework. Within this framework, both a patient agent and a coaching agent collaboratively support medical learners in practicing their medical communication skills during consultations. Unlike traditional dialogue systems, ChatCoach provides a simulated environment where a human doctor can engage in medical dialogue with a patient agent. Simultaneously, a coaching agent provides real-time feedback to the doctor. To construct the ChatCoach system, we developed a dataset and integrated Large Language Models such as ChatGPT and Llama2, aiming to assess their effectiveness in communicative medical coaching tasks. Our comparative analysis demonstrates that instruction-tuned Llama2 significantly outperforms ChatGPT's prompting-based approaches.