Multimodal sentiment analysis holds significant importance within the realm of human-computer interaction. Due to the ease of collecting unlabeled online resources compared to the high costs associated with annotation, it becomes imperative for researchers to develop semi-supervised methods that leverage unlabeled data to enhance model performance. Existing semi-supervised approaches, particularly those applied to trivial image classification tasks, are not suitable for multimodal regression tasks due to their reliance on task-specific augmentation and thresholds designed for classification tasks. To address this limitation, we propose the Multimodal Consistency-based Teacher (MC-Teacher), which incorporates consistency-based pseudo-label technique into semi-supervised multimodal sentiment analysis. In our approach, we first propose synergistic consistency assumption which focus on the consistency among bimodal representation. Building upon this assumption, we develop a learnable filter network that autonomously learns how to identify misleading instances instead of threshold-based methods. This is achieved by leveraging both the implicit discriminant consistency on unlabeled instances and the explicit guidance on constructed training data with labeled instances. Additionally, we design the self-adaptive exponential moving average strategy to decouple the student and teacher networks, utilizing a heuristic momentum coefficient. Through both quantitative and qualitative experiments on two benchmark datasets, we demonstrate the outstanding performances of the proposed MC-Teacher approach. Furthermore, detailed analysis experiments and case studies are provided for each crucial component to intuitively elucidate the inner mechanism and further validate their effectiveness.