Even though neural networks have been long deployed in applications involving tabular data, still existing neural architectures are not explainable by design. In this paper, we propose a new class of interpretable neural networks for tabular data that are both deep and linear at the same time (i.e. mesomorphic). We optimize deep hypernetworks to generate explainable linear models on a per-instance basis. As a result, our models retain the accuracy of black-box deep networks while offering free-lunch explainability for tabular data by design. Through extensive experiments, we demonstrate that our explainable deep networks have comparable performance to state-of-the-art classifiers on tabular data and outperform current existing methods that are explainable by design.