This work explores the utility of explicit structure for representation learning in NLP by developing StrAE -- an autoencoding framework that faithfully leverages sentence structure to learn multi-level node embeddings in an unsupervised fashion. We use StrAE to train models across different types of sentential structure and objectives, including a novel contrastive loss over structure, and evaluate the learnt embeddings on a series of both intrinsic and extrinsic tasks. Our experiments indicate that leveraging explicit structure through StrAE leads to improved embeddings over prior work, and that our novel contrastive objective over structure outperforms the standard cross-entropy objective. Moreover, in contrast to findings from prior work that weakly leverages structure, we find that being completely faithful to structure does enable disambiguation between types of structure based on the corresponding model's performance. As further evidence of StrAE's utility, we develop a simple proof-of-concept approach to simultaneously induce structure while learning embeddings, rather than being given structure, and find that performance is comparable to that of the best-performing models where structure is given. Finally, we contextualise these results by comparing StrAE against standard unstructured baselines learnt in similar settings, and show that faithfully leveraging explicit structure can be beneficial in lexical and sentence-level semantics.