Pain is an essential physiological phenomenon of human beings. Accurate assessment of pain is important to develop proper treatment. Although self-report method is the gold standard in pain assessment, it is not applicable to individuals with communicative impairment. Non-verbal pain indicators such as pain related facial expressions and changes in physiological parameters could provide valuable insights for pain assessment. In this paper, we propose a multimodal-based Stream Integrated Neural Network with Different Frame Rates (SINN) that combines facial expression and biomedical signals for automatic pain assessment. The main contributions of this research are threefold. (1) There are four-stream inputs of the SINN for facial expression feature extraction. The variant facial features are integrated with biomedical features, and the joint features are utilized for pain assessment. (2) The dynamic facial features are learned in both implicit and explicit manners to better represent the facial changes that occur during pain experience. (3) Multiple modalities are utilized to identify various pain states, including facial expression and biomedical signals. The experiments are conducted on publicly available pain datasets, and the performance is compared with several deep learning models. The experimental results illustrate the superiority of the proposed model, and it achieves the highest accuracy of 68.2%, which is up to 5% higher than the basic deep learning models on pain assessment with binary classification.