Integrating multiple online social networks (OSNs) has important implications for many downstream social mining tasks, such as user preference modelling, recommendation, and link prediction. However, it is unfortunately accompanied by growing privacy concerns about leaking sensitive user information. How to fully utilize the data from different online social networks while preserving user privacy remains largely unsolved. To this end, we propose a Cross-network Social User Embedding framework, namely DP-CroSUE, to learn the comprehensive representations of users in a privacy-preserving way. We jointly consider information from partially aligned social networks with differential privacy guarantees. In particular, for each heterogeneous social network, we first introduce a hybrid differential privacy notion to capture the variation of privacy expectations for heterogeneous data types. Next, to find user linkages across social networks, we make unsupervised user embedding-based alignment in which the user embeddings are achieved by the heterogeneous network embedding technology. To further enhance user embeddings, a novel cross-network GCN embedding model is designed to transfer knowledge across networks through those aligned users. Extensive experiments on three real-world datasets demonstrate that our approach makes a significant improvement on user interest prediction tasks as well as defending user attribute inference attacks from embedding.