Vision-Language Models (VLMs) generate discourse-level, multi-sentence visual descriptions, challenging text scene graph parsers built for single-sentence caption-to-graph mapping. Current approaches typically merge sentence-level parsing outputs for discourse input, often missing phenomena like cross-sentence coreference, resulting in fragmented graphs and degraded downstream VLM task performance. We introduce a new task, Discourse-level text Scene Graph parsing (DiscoSG), and release DiscoSG-DS, a dataset of 400 expert-annotated and 8,430 synthesised multi-sentence caption-graph pairs. Each caption averages 9 sentences, and each graph contains at least 3× more triples than those in existing datasets. Fine-tuning GPT-4o on DiscoSG-DS yields over 40% higher SPICE than the strongest sentence-merging baseline. However, its high inference cost and licensing restrict open-source use, and smaller fine-tuned open-source models (e.g., Flan-T5) perform poorly on dense graph generation. To bridge this gap, we propose DiscoSG-Refiner, which drafts a base graph using a seed parser and iteratively refines it with a second model, improving robustness for complex graph generation. Using two small fine-tuned Flan-T5-Base models, DiscoSG-Refiner improves SPICE by ~30% over the baseline while achieving 86× faster inference than GPT-4o. It also delivers consistent gains on downstream VLM tasks, including discourse-level caption evaluation and hallucination detection, outperforming alternative parsers. Code and data are available at https://github.com/ShaoqLin/DiscoSG .