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U-shaped networks are widely used in various medical image tasks, such as segmentation, restoration and reconstruction, but most of them usually rely on centralized learning and thus ignore privacy issues. To address the privacy concerns, federated learning (FL) and split learning (SL) have attracted increasing attention. However, it is hard for both FL and SL to balance the local computational cost, model privacy and parallel training simultaneously. To achieve this goal, in this paper, we propose Robust Split Federated Learning (RoS-FL) for U-shaped medical image networks, which is a novel hybrid learning paradigm of FL and SL. Previous works cannot preserve the data privacy, including the input, model parameters, label and output simultaneously. To effectively deal with all of them, we design a novel splitting method for U-shaped medical image networks, which splits the network into three parts hosted by different parties. Besides, the distributed learning methods usually suffer from a drift between local and global models caused by data heterogeneity. Based on this consideration, we propose a dynamic weight correction strategy (\textbf{DWCS}) to stabilize the training process and avoid model drift. Specifically, a weight correction loss is designed to quantify the drift between the models from two adjacent communication rounds. By minimizing this loss, a correction model is obtained. Then we treat the weighted sum of correction model and final round models as the result. The effectiveness of the proposed RoS-FL is supported by extensive experimental results on different tasks. Related codes will be released at https://github.com/Zi-YuanYang/RoS-FL.