Information networks are ubiquitous in many applications. A popular way to facilitate the information in a network is to embed the network structure into low-dimension spaces where each node is represented as a vector. The learned representations have been proven to advance various network analysis tasks such as link prediction and node classification. The majority of existing embedding algorithms are designed for the networks with one type of nodes and one dimension of relations among nodes. However, many networks in the real-world complex systems have multiple types of nodes and multiple dimensions of relations. For example, an e-commerce network can have users and items, and items can be viewed or purchased by users, corresponding to two dimensions of relations. In addition, some types of nodes can present hierarchical structure. For example, authors in publication networks are associated to affiliations; and items in e-commerce networks belong to categories. Most of existing methods cannot be naturally applicable to these networks. In this paper, we aim to learn representations for networks with multiple dimensions and hierarchical structure. In particular, we provide an approach to capture independent information from each dimension and dependent information across dimensions and propose a framework MINES, which performs Multi-dImension Network Embedding with hierarchical Structure. Experimental results on a network from a real-world e-commerce website demonstrate the effectiveness of the proposed framework.