Corruptions due to data perturbations and label noise are prevalent in the datasets from unreliable sources, which poses significant threats to model training. Despite existing efforts in developing robust models, current learning methods commonly overlook the possible co-existence of both corruptions, limiting the effectiveness and practicability of the model. In this paper, we develop an Effective and Robust Adversarial Training (ERAT) framework to simultaneously handle two types of corruption (i.e., data and label) without prior knowledge of their specifics. We propose a hybrid adversarial training surrounding multiple potential adversarial perturbations, alongside a semi-supervised learning based on class-rebalancing sample selection to enhance the resilience of the model for dual corruption. On the one hand, in the proposed adversarial training, the perturbation generation module learns multiple surrogate malicious data perturbations by taking a DNN model as the victim, while the model is trained to maintain semantic consistency between the original data and the hybrid perturbed data. It is expected to enable the model to cope with unpredictable perturbations in real-world data corruption. On the other hand, a class-rebalancing data selection strategy is designed to fairly differentiate clean labels from noisy labels. Semi-supervised learning is performed accordingly by discarding noisy labels. Extensive experiments demonstrate the superiority of the proposed ERAT framework.