We introduce a novel type of text representation that preserves the 2D layout of a document. This is achieved by encoding each document page as a two-dimensional grid of characters. Based on this representation, we present a generic document understanding pipeline for structured documents. This pipeline makes use of a fully convolutional encoder-decoder network that predicts a segmentation mask and bounding boxes. We demonstrate its capabilities on an information extraction task from invoices and show that it significantly outperforms approaches based on sequential text or document images.