Automated parsing of scanned documents into richly structured, machine-readable formats remains a critical bottleneck in Document AI, as traditional multi-stage pipelines suffer from error propagation and limited adaptability to diverse layouts. We introduce layoutRL, an end-to-end reinforcement learning framework that trains models to be explicitly layout-aware by optimizing a composite reward of normalized edit distance, paragraph count accuracy, and reading order preservation. Leveraging our newly released dataset, Infinity-Doc-55K, which combines 55K high-fidelity synthetic scanned document parsing data with expert-filtered real-world documents, we instantiate layoutRL in a vision-language-model-based parser called Infinity-Parser. Evaluated on English and Chinese benchmarks for OCR, table and formula extraction, and reading order detection, Infinity-Parser achieves new state-of-the-art performance in both accuracy and structural fidelity, outpacing specialist pipelines and general-purpose vision-language models. We will publicly release our code and dataset to accelerate progress in robust document understanding.