Network embedding has been increasingly employed in network analysis as it can learn node representations that encode the network structure resulting from node interactions. In this paper, we propose to embed not only the network structure, but also the interaction content within which each interaction arises. The interaction content should better be embedded in node representations because it reveals interaction preferences of the two nodes involved, and interaction preferences are essential characteristics that nodes expose in the network environment. To achieve this goal, we propose an idea of interaction content-aware network embedding via co-embedding of nodes and edges. The embedding of edges is to learn edge representations that preserve the interaction content. Then the interaction content can be incorporated into node representations through edge representations. Comprehensive empirical evaluation demonstrates that the proposed method outperforms five recent network embedding models in applications including visualization, link prediction and classification.