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Domain generalization (DG) aims to learn a generalizable model from multiple training domains such that it can perform well on unseen target domains. A popular strategy is to augment training data to benefit generalization through methods such as Mixup~\cite{zhang2018mixup}. While the vanilla Mixup can be directly applied, theoretical and empirical investigations uncover several shortcomings that limit its performance. Firstly, Mixup cannot effectively identify the domain and class information that can be used for learning invariant representations. Secondly, Mixup may introduce synthetic noisy data points via random interpolation, which lowers its discrimination capability. Based on the analysis, we propose a simple yet effective enhancement for Mixup-based DG, namely domain-invariant Feature mIXup (FIX). It learns domain-invariant representations for Mixup. To further enhance discrimination, we leverage existing techniques to enlarge margins among classes to further propose the domain-invariant Feature MIXup with Enhanced Discrimination (FIXED) approach. We present theoretical insights about guarantees on its effectiveness. Extensive experiments on seven public datasets across two modalities including image classification (Digits-DG, PACS, Office-Home) and time series (DSADS, PAMAP2, UCI-HAR, and USC-HAD) demonstrate that our approach significantly outperforms nine state-of-the-art related methods, beating the best performing baseline by 6.5\% on average in terms of test accuracy. Code is available at: https://github.com/jindongwang/transferlearning/tree/master/code/deep/fixed.