Graph neural networks (GNNs) have been widely used in deep learning on graphs. They can learn effective node representations that achieve superior performances in graph analysis tasks such as node classification and node clustering. However, most methods ignore the heterogeneity in real-world graphs. Methods designed for heterogeneous graphs, on the other hand, fail to learn complex semantic representations because they only use meta-paths instead of meta-graphs. Furthermore, they cannot fully capture the content-based correlations between nodes, as they either do not use the self-attention mechanism or only use it to consider the immediate neighbors of each node, ignoring the higher-order neighbors. We propose a novel Higher-order Attribute-Enhancing (HAE) framework that enhances node embedding in a layer-by-layer manner. Under the HAE framework, we propose a Higher-order Attribute-Enhancing Graph Neural Network (HAEGNN) for heterogeneous network representation learning. HAEGNN simultaneously incorporates meta-paths and meta-graphs for rich, heterogeneous semantics, and leverages the self-attention mechanism to explore content-based nodes interactions. The unique higher-order architecture of HAEGNN allows examining the first-order as well as higher-order neighborhoods. Moreover, HAEGNN shows good explainability as it learns the importances of different meta-paths and meta-graphs. HAEGNN is also memory-efficient, for it avoids per meta-path based matrix calculation. Experimental results not only show HAEGNN superior performance against the state-of-the-art methods in node classification, node clustering, and visualization, but also demonstrate its superiorities in terms of memory efficiency and explainability.