A key challenge in eXplainable Artificial Intelligence is the well-known tradeoff between the transparency of an algorithm (i.e., how easily a human can directly understand the algorithm, as opposed to receiving a post-hoc explanation), and its accuracy. We report on the design of a new deep network that achieves improved transparency without sacrificing accuracy. We design a deep convolutional neuro-fuzzy inference system (DCNFIS) by hybridizing fuzzy logic and deep learning models and show that DCNFIS performs as accurately as three existing convolutional neural networks on four well-known datasets. We furthermore that DCNFIS outperforms state-of-the-art deep fuzzy systems. We then exploit the transparency of fuzzy logic by deriving explanations, in the form of saliency maps, from the fuzzy rules encoded in DCNFIS. We investigate the properties of these explanations in greater depth using the Fashion-MNIST dataset.