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Graph Convolutional Neural Networks (GCNs) have become effective machine learning algorithms for many downstream network mining tasks such as node classification, link prediction, and community detection. However, most GCN methods have been developed for homogenous networks and are limited to a single embedding for each node. Complex systems, often represented by heterogeneous, multiplex networks present a more difficult challenge for GCN models and require that such techniques capture the diverse contexts and assorted interactions that occur between nodes. In this work, we propose RAHMeN, a novel unified relation-aware embedding framework for attributed heterogeneous multiplex networks. Our model incorporates node attributes, motif-based features, relation-based GCN approaches, and relational self-attention to learn embeddings of nodes with respect to the various relations in a heterogeneous, multiplex network. In contrast to prior work, RAHMeN is a more expressive embedding framework that embraces the multi-faceted nature of nodes in such networks, producing a set of multi-embeddings that capture the varied and diverse contexts of nodes. We evaluate our model on four real-world datasets from Amazon, Twitter, YouTube, and Tissue PPIs in both transductive and inductive settings. Our results show that RAHMeN consistently outperforms comparable state-of-the-art network embedding models, and an analysis of RAHMeN's relational self-attention demonstrates that our model discovers interpretable connections between relations present in heterogeneous, multiplex networks.