Despite their performance, Artificial Neural Networks are not reliable enough for most of industrial applications. They are sensitive to noises, rotations, blurs and adversarial examples. There is a need to build defenses that protect against a wide range of perturbations, covering the most traditional common corruptions and adversarial examples. We propose a new data augmentation strategy called M-TLAT and designed to address robustness in a broad sense. Our approach combines the Mixup augmentation and a new adversarial training algorithm called Targeted Labeling Adversarial Training (TLAT). The idea of TLAT is to interpolate the target labels of adversarial examples with the ground-truth labels. We show that M-TLAT can increase the robustness of image classifiers towards nineteen common corruptions and five adversarial attacks, without reducing the accuracy on clean samples.