As global cross-lingual communication intensifies, language barriers in visually rich documents such as PDFs remain a practical bottleneck. Existing document translation pipelines face a tension between linguistic processing and layout preservation: text-oriented Computer-Assisted Translation (CAT) systems often discard structural metadata, while document parsers focus on extraction and do not support faithful re-rendering after translation. We introduce BabelDOC, an Intermediate Representation (IR)-based framework for layout-preserving PDF translation. BabelDOC decouples visual layout metadata from semantic content, enabling document-level translation operations such as terminology extraction, cross-page context handling, glossary-constrained generation, and formula placeholdering. The translated content is then re-anchored to the original layout through an adaptive typesetting engine. Experiments on a curated 200-page benchmark, together with human evaluation and multimodal LLM-as-a-judge evaluation, show that BabelDOC improves layout fidelity, visual aesthetics, and terminology consistency over representative baselines, while maintaining competitive translation precision. The open-source toolkit and its interactive downstream applications have garnered over 7.8k stars on GitHub https://github.com/funstory-ai/BabelDOC. A demonstration video is available at https://youtu.be/chwrlApH7a4.