Large volumes of data required to train accurate deep neural networks (DNNs) are seldom available with any single entity. Often, privacy concerns and stringent data regulations prevent entities from sharing data with each other or with a third-party learning service provider. While cross-silo federated learning (FL) allows collaborative learning of large DNNs without sharing the data itself, most existing cross-silo FL algorithms have an unacceptable utility-privacy trade-off. In this work, we propose a framework called Confidential and Private Decentralized (CaPriDe) learning, which optimally leverages the power of fully homomorphic encryption (FHE) to enable collaborative learning without compromising on the confidentiality and privacy of data. In CaPriDe learning, participating entities release their private data in an encrypted form allowing other participants to perform inference in the encrypted domain. The crux of CaPriDe learning is mutual knowledge distillation between multiple local models through a novel distillation loss, which is an approximation of the Kullback-Leibler (KL) divergence between the local predictions and encrypted inferences of other participants on the same data that can be computed in the encrypted domain. Extensive experiments on three datasets show that CaPriDe learning can improve the accuracy of local models without any central coordination, provide strong guarantees of data confidentiality and privacy, and has the ability to handle statistical heterogeneity. Constraints on the model architecture (arising from the need to be FHE-friendly), limited scalability, and computational complexity of encrypted domain inference are the main limitations of the proposed approach. The code can be found at https://github.com/tnurbek/capride-learning.