In the realm of healthcare where decentralized facilities are prevalent, machine learning faces two major challenges concerning the protection of data and models. The data-level challenge concerns the data privacy leakage when centralizing data with sensitive personal information. While the model-level challenge arises from the heterogeneity of local models, which need to be collaboratively trained while ensuring their confidentiality to address intellectual property concerns. To tackle these challenges, we propose a new framework termed Abstention-Aware Federated Voting (AAFV) that can collaboratively and confidentially train heterogeneous local models while simultaneously protecting the data privacy. This is achieved by integrating a novel abstention-aware voting mechanism and a differential privacy mechanism onto local models' predictions. In particular, the proposed abstention-aware voting mechanism exploits a threshold-based abstention method to select high-confidence votes from heterogeneous local models, which not only enhances the learning utility but also protects model confidentiality. Furthermore, we implement AAFV on two practical prediction tasks of diabetes and in-hospital patient mortality. The experiments demonstrate the effectiveness and confidentiality of AAFV in testing accuracy and privacy protection.