With the rise of online social media, users from across the world can participate in opinion formation processes, and some discussions lead to controversial debates around this phenomenon. Controversy detection in social media can help explore public discourse spaces and understand topical issues. Previous controversial detection studies focus more on identifying the opinion or emotional orientation of a comment, while we focus on whether there is a controversial relationship between a comment and its replies. Here, we collect a dataset consisting of 511 news articles, 103,787 comments, and 71,579 users on the Chinese social media platform, Toutiao, and we study the controversial interactions on the subsets of this dataset. Our approach treats news, comments, and users as different types of nodes and constructs multiplex networks connected by user–comment links (i.e., publishing relationship), comment–news links (i.e., comment relationship), and comment–comment links (i.e., replying relationship). Furthermore, we propose a model based on deep learning to detect controversial interactions from these multiplex networks. Our supervised model achieves 83.24% accuracy, with an improvement compared to competitive models. Moreover, we illustrate the applicability of our approach using different ratios of training and testing sets. Our results demonstrate the usefulness of the multiplex networks model for controversial interaction detection and provide a new perspective on controversy detection problems.