Dependency-based graph convolutional networks (DepGCNs) are proven helpful for text representation to handle many natural language tasks. Almost all previous models are trained with cross-entropy (CE) loss, which maximizes the posterior likelihood directly. However, the contribution of dependency structures is not well considered by CE loss. As a result, the performance improvement gained by using the structure information can be narrow due to the failure in learning to rely on this structure information. To face the challenge, we propose the novel structurally comparative hinge (SCH) loss function for DepGCNs. SCH loss aims at enlarging the margin gained by structural representations over non-structural ones. From the per- spective of information theory, this is equivalent to improving the conditional mutual information of model decision and structure information given text. Our experimental results on both English and Chinese datasets show that by substituting SCH loss for CE loss on various tasks, for both induced structures and structures from an external parser, performance is improved without additional learnable parameters. Furthermore, the extent to which certain types of examples rely on the dependency structure can be measured directly by the learned margin, which results in better interpretability. In addition, through detailed analysis, we show that this structure margin has a positive correlation with task performance and structure induction of DepGCNs, and SCH loss can help model focus more on the shortest dependency path between entities. We achieve the new state-of-the-art results on TACRED, IMDB, and Zh. Literature datasets, even compared with ensemble and BERT baselines.