The process monitoring method for industrial production can technically achieve early warning of abnormal situations and help operators make timely and reliable response decisions. Because practical industrial processes have multimodal operating conditions, the data distributions of process variables are different. The different data distributions may cause the fault detection model to be invalid. In addition, the fault diagnosis model cannot find the correct root cause variable of system failure by only identifying abnormal variables. There are correlations between the trend states of the process variables. If we do not consider these correlations, this may result in an incorrect fault root cause. Therefore, multimodal industrial process monitoring is a tough issue. In this paper, we propose a three-step framework for multimodal industrial process monitoring. The framework aims for multimodal industrial processes to detect the faulty status timely and then find the correct root variable that causes the failure. We present deep local adaptive network (DLAN), two-stage qualitative trend analysis (TSQTA), and five-state Bayesian network (FSBN) to implement fault detection, identification, and diagnosis step by step. This framework can detect the system failure timely, identify abnormal variables, and find the root cause variable and the fault propagation path. The case studies on the Tennessee Eastman simulation and a practical chlorobenzene production process are provided to verify the effectiveness of the proposed framework in multimodal industrial process monitoring.