To improve the accessibility of smart devices and to simplify their usage, building models which understand user interfaces (UIs) and assist users to complete their tasks is critical. However, unique challenges are proposed by UI-specific characteristics, such as how to effectively leverage multimodal UI features that involve image, text, and structural metadata and how to achieve good performance when high-quality labeled data is unavailable. To address such challenges we introduce UIBert, a transformer-based joint image-text model trained through novel pre-training tasks on large-scale unlabeled UI data to learn generic feature representations for a UI and its components. Our key intuition is that the heterogeneous features in a UI are self-aligned, i.e., the image and text features of UI components, are predictive of each other. We propose five pretraining tasks utilizing this self-alignment among different features of a UI component and across various components in the same UI. We evaluate our method on nine real-world downstream UI tasks where UIBert outperforms strong multimodal baselines by up to 9.26% accuracy.