Facade parsing aims to decompose a building facade image into semantic regions of the facade objects. Considering each architectural element on a facade as a parameterized rectangle, we formulate the facade parsing task as object detection, allowing overlapping and nesting, which will support structural 3D modeling and editing for further applications. In contrast to general object detection, the spatial arrangement regularity and appearance similarity between the facade elements of the same category provide valuable context for accurate element localization. In this paper, we propose to exploit the spatial arrangement regularity and appearance similarity of facade elements in a detection framework. Our element-arrangement context network (EACNet) consists of two unidirectional attention branches, one to capture the column-context and the other to capture row-context to aggregate element-specific features from multiple instances on the facade. We conduct extensive experiments on four public datasets (ECP, CMP, Graz50, and eTRIMS). The proposed EACNet achieves the highest mIoU (82.1% on ECP, 77.35% on Graz50, and 82.3% on eTRIMS) compared with the state-of-the-art methods. Both the quantitative and qualitative evaluation results demonstrate the effectiveness of our dual unidirectional attention branches to parse facade elements.