Federated learning (FL) is receiving much attention in the Healthcare Internet of Things (H-IoT) to support various instantaneous E-health services. Today, the deployment of FL suffers from several challenges, such as high training latency and data privacy leakage risks, especially for resource-constrained medical devices. In this article, we develop a three-layer FL architecture to decrease training latency by introducing split learning into FL. We formulate a long-term optimization problem to minimize the local model training latency while preserving the privacy of the original medical data in H-IoT. Specially, a Privacy-ware Model Partitioning Algorithm (PMPA) is proposed to solve the formulated problem based on the Lyapunov optimization theory. In PMPA, the local model is partitioned properly between a resource-constrained medical end device and an edge server, which meets privacy requirements and energy consumption constraints. The proposed PMPA is separated into two phases. In the first phase, a partition point set is obtained using Kullback-Leibler (KL) divergence to meet the privacy requirement. In the second phase, we employ the model partitioning function, derived through Lyapunov optimization, to select the partition point from the partition point set that that satisfies the energy consumption constraints. Simulation results show that compared with traditional FL, the proposed algorithm can significantly reduce the local training latency. Moreover, the proposed algorithm improves the efficiency of medical image classification while ensuring medical data security.