Interpolation-based Data Augmentation (DA) methods (Mixup) linearly interpolate the inputs and labels of two or more training examples. Mixup has more recently been adapted to the field of Natural Language Processing (NLP), mainly for sequence labeling tasks. However, such a simple adoption yields mixed or unstable improvements over the baseline models. We argue that the direct-adoption methods do not account for structures in NLP tasks. To this end, we propose SegMix, a collection of interpolation-based DA algorithms that can adapt to task-specific structures. SegMix poses fewer constraints on data structures, is robust to various hyperparameter settings, applies to more task settings, and adds little computational overhead. In the algorithm's core, we apply interpolation methods on task-specific meaningful segments, in contrast to applying them on sequences as in prior work. We find SegMix to be a flexible framework that combines rule-based DA methods with interpolation-based methods, creating interesting mixtures of DA techniques. We show that SegMix consistently improves performance over strong baseline models in Named Entity Recognition (NER) and Relation Extraction (RE) tasks, especially under data-scarce settings. Furthermore, this method is easy to implement and adds negligible training overhead.