This paper presents an adaptive 5G-and-beyond network-enabled interpretable federated learning (FL) framework enhanced by neuroevolution for mobile telemedicine systems. The framework aims to improve communication efficiency, interpretability, and reduce complexity in FL for medical image processing. The key contributions include: (1) an adaptive communication scheduling scheme that reduces communication burden by uploading local model information based on training status; (2) an interpretable convolutional fuzzy rough neural network (CFRNN) model, which replaces the final expand layer with a fuzzification layer, forming fuzzy rules and defining rough membership degrees; and (3) a flexible neural architecture search (NAS) space with a memetic multiobjective evolutionary algorithm (MOEA) that optimizes validation accuracy while considering model complexity. The framework integrates smart scheduling, interpretable fuzzy rough logic, and neuroevolution. It is shown to improve communication efficiency, increase interpretability of diagnosis with protected privacy, and generate low-complexity neural architectures. The paper discusses the challenges of mobile healthcare, including information security, privacy protection, and diagnostic accuracy, and highlights the potential of FL in addressing these issues. FL allows multi-institutional cooperation without transmitting patient data, enabling indirect medical data sharing. The framework is applied to medical image analysis, such as ultrasound, 3D brain imaging, chest X-rays, and CT scans. The paper also discusses the use of convolutional neural networks (CNNs) in medical imaging and the challenges of interpretability in deep learning models. Neuroevolution is used to automatically search for neural network architectures and hyperparameters, enabling multiobjective optimization. The proposed framework is designed to address the communication efficiency, interpretability, and neuroevolution issues in FL, providing a reliable solution for mobile telemedicine systems.This paper presents an adaptive 5G-and-beyond network-enabled interpretable federated learning (FL) framework enhanced by neuroevolution for mobile telemedicine systems. The framework aims to improve communication efficiency, interpretability, and reduce complexity in FL for medical image processing. The key contributions include: (1) an adaptive communication scheduling scheme that reduces communication burden by uploading local model information based on training status; (2) an interpretable convolutional fuzzy rough neural network (CFRNN) model, which replaces the final expand layer with a fuzzification layer, forming fuzzy rules and defining rough membership degrees; and (3) a flexible neural architecture search (NAS) space with a memetic multiobjective evolutionary algorithm (MOEA) that optimizes validation accuracy while considering model complexity. The framework integrates smart scheduling, interpretable fuzzy rough logic, and neuroevolution. It is shown to improve communication efficiency, increase interpretability of diagnosis with protected privacy, and generate low-complexity neural architectures. The paper discusses the challenges of mobile healthcare, including information security, privacy protection, and diagnostic accuracy, and highlights the potential of FL in addressing these issues. FL allows multi-institutional cooperation without transmitting patient data, enabling indirect medical data sharing. The framework is applied to medical image analysis, such as ultrasound, 3D brain imaging, chest X-rays, and CT scans. The paper also discusses the use of convolutional neural networks (CNNs) in medical imaging and the challenges of interpretability in deep learning models. Neuroevolution is used to automatically search for neural network architectures and hyperparameters, enabling multiobjective optimization. The proposed framework is designed to address the communication efficiency, interpretability, and neuroevolution issues in FL, providing a reliable solution for mobile telemedicine systems.