Data mining, integration, and utilization are the inevitable trend of the Internet of Medical Things (IoMT) in the context of big data. With the increasing demand for data privacy, federated learning has emerged as a new paradigm, which enables distributed joint training of medical data sources without leaving the private domain. However, federated learning is suffering from security threats as the shared local model will reveal original datasets. Privacy leakage is even more fatal in healthcare because medical data contains critically sensitive information. In addition, open wireless channels are susceptible to malicious attacks. To further safeguard the privacy of IoMT, we propose a comprehensive privacy-preserving federated learning scheme with a tactful dropout handling mechanism. The proposed scheme leverages blind masking and certificateless proxy re-encryption (CL-PRE) for secure aggregation, ensuring the confidentiality of the local model and rendering the global model invisible to any parties other than clients. It also provides authentication of uploaded models while protecting identity privacy. Compared with other relevant schemes, our solution has better performance on functional features and efficiency, and is more applicable to IoMT systems with many devices.