As there are various data mining applications involving network analysis, network embedding is frequently employed to learn latent representations or embeddings that encode the network structure. However, existing network embedding models are only designed for a single network scenario. It is common that nodes can have multiple types of relationships in big data era, which results in multiple networks, e.g., multiple social networks and multiple gene regulatory networks. Jointly embedding multiple networks thus may make network-specific embeddings more comprehensive and complete as the same node may expose similar or complementary characteristics in different networks. In this paper, we thus propose an idea of multi-task network embedding (MTNE) to jointly learn multiple network-specific embeddings for each node via enforcing an extra information-sharing embedding. Moreover, we instantiate the idea in two models that are different in the mechanism for enforcing the information-sharing embedding. The first model enforces the information-sharing embedding as a common embedding shared by all tasks, which is similar to the concept of the common metric in multi-task metric learning while the second model enforces the information-sharing embedding as a consensus embedding on which all network-specific embeddings agree. We demonstrate through comprehensive experiments on three real-world datasets that the proposed models outperform state-of-the-art network embedding models in applications including visualization, link prediction, and multi-label classification.