We study the problem of representation learning for multiple types of entities in a co-ordered network where order relations exist among entities of the same type, and association relations exist across entities of different types. The key challenge in learning co-ordered network embedding is to preserve order relations among entities of the same type while leveraging on the general consistency in order relations between different entity types. In this paper, we propose an embedding model, CO2Vec, that addresses this challenge using mutually reinforced order dependencies. Specifically, CO2Vec explores in-direct order dependencies as supplementary evidence to enhance order representation learning across different types of entities. We conduct extensive experiments on both synthetic and real world datasets to demonstrate the robustness and effectiveness of CO2Vec against several strong baselines in link prediction task. We also design a comprehensive evaluation framework to study the performance of CO2Vec under different settings. In particular, our results show the robustness of CO2Vec with the removal of order relations from the original networks.