In the evolving application of medical artificial intelligence, federated learning is notable for its ability to protect training data privacy. Federated learning facilitates collaborative model development without the need to share local data from healthcare institutions. Yet, the statistical and system heterogeneity among these institutions poses substantial challenges, which affects the effectiveness of federated learning and hampers the exchange of information between clients. To address these issues, we introduce a novel approach, MH-pFLGB, which employs a global bypass strategy to mitigate the reliance on public datasets and navigate the complexities of non-IID data distributions. Our method enhances traditional federated learning by integrating a global bypass model, which would share the information among the clients, but also serves as part of the network to enhance the performance on each client. Additionally, MH-pFLGB provides a feature fusion module to better combine the local and global features. We validate \model{}'s effectiveness and adaptability through extensive testing on different medical tasks, demonstrating superior performance compared to existing state-of-the-art methods.