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This paper proposes a simple yet effective interpolation-based data augmentation approach termed DoubleMix, to improve the robustness of models in text classification. DoubleMix first leverages a couple of simple augmentation operations to generate several perturbed samples for each training data, and then uses the perturbed data and original data to carry out a two-step interpolation in the hidden space of neural models. Concretely, it first mixes up the perturbed data to a synthetic sample and then mixes up the original data and the synthetic perturbed data. DoubleMix enhances models' robustness by learning the "shifted" features in hidden space. On six text classification benchmark datasets, our approach outperforms several popular text augmentation methods including token-level, sentence-level, and hidden-level data augmentation techniques. Also, experiments in low-resource settings show our approach consistently improves models' performance when the training data is scarce. Extensive ablation studies and case studies confirm that each component of our approach contributes to the final performance and show that our approach exhibits superior performance on challenging counterexamples. Additionally, visual analysis shows that text features generated by our approach are highly interpretable. Our code for this paper can be found at https://github.com/declare-lab/DoubleMix.git.