Privacy-preserving decentralized federated learning (DFL) has been extensively studied to protect the privacy of both data and models. Meanwhile, researchers have developed various efficient aggregation rules to defend DFL against poisoning attacks from Byzantine adversaries. However, existing techniques fail to effectively address the coexistence of model privacy and Byzantine robustness in decentralized scenarios. To bridge this gap, we propose BP-DFL, a novel DFL scheme that simultaneously detects malicious models while preserving model privacy. Our approach integrates functional secret sharing and multi-party homomorphic encryption schemes to design a secure model verification and aggregation protocol. Unlike existing solutions based on differential privacy, our scheme avoids noise injection and ensures model consistency throughout the protocol. Furthermore, we ensure that clients remain unaware of which neighbors' models are aggregated or discarded, thereby preventing clients from compromising the privacy of neighbors' models through selective aggregation. We provide formal security proofs for BP-DFL against Byzantine clients. Experimental results show that existing aggregation rules suffer from poor performance in defending against Byzantine poisoning attacks with the introduction of differential privacy noise, whereas BP-DFL achieves higher and more stable model accuracy by a substantial margin.