Vision-Language Models (VLMs) now generate discourse-level, multi-sentence visual descriptions, challenging text scene graph parsers originally designed 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. To address this, we introduce textbfDiscourse-level text textbfScene textbfGraph parsing (DiscoSG), supported by our dataset DiscoSG-DS, which comprises 400 expert-annotated and 8,430 synthesized multi-sentence caption–graph pairs for images. Each graph contains sim15times more objects and relations per caption than prior datasets. While fine-tuning large PLMs (i.e., GPT-4o) on DiscoSG-DS improves SPICE by sim 48% over the best sentence-merging baseline, high inference cost and restrictive licensing hinder its open-source use, and smaller fine-tuned PLMs struggle with complex graphs. We propose DiscoSG-Refiner, which drafts a base graph using one small PLM, then employs a second PLM to iteratively propose graph edits, reducing full-graph generation overhead. Using two Flan-T5-BASE models, DiscoSG-Refiner still improves SPICE by sim 30% over the best baseline while achieving 86times faster inference than GPT-4o. It also consistently improves downstream VLM tasks like discourse-level caption evaluation and hallucination detection. Code and data are available at~\url{https://anonymous.4open.science/r/DiscoSG/}.