Language Models (LMs) often struggle with linguistic understanding at the discourse level, even though discourse patterns such as coherence, cohesion, and narrative flow are prevalent in their pre-training data. Current methods address these challenges only after the pre-training phase, relying on expensive human annotated data to align the model. To improve the discourse capabilities of LMs already at the pre-training stage, we introduce DEPTH, an encoder-decoder model that learns to represent sentences using a discourse-oriented pre-training objective. DEPTH combines hierarchical sentence representations with two objectives: (1) Sentence Un-Shuffling, and (2) Span-Corruption. This approach trains the model to represent both sub-word-level and sentence-level dependencies over a massive amount of unstructured text. When trained either from scratch or continuing from a pre-trained T5 checkpoint, DEPTH learns semantic and discourse-level representations faster than T5, outperforming it in span-corruption loss despite the additional sentence-un-shuffling objective. Evaluations on the GLUE, DiscoEval, and NI benchmarks demonstrate DEPTH's ability to quickly learn diverse downstream tasks, which require syntactic, semantic, and discourse capabilities. Overall, our approach extends the discourse capabilities of T5, while minimally impacting other natural language understanding (NLU) capabilities in the resulting LM.