The absence of tactile cues such as keys and buttons makes touchscreens difficult to navigate for people with visual impairments. Increasing tactile feedback and tangible interaction on touchscreens can improve their accessibility. However, prior solutions have either required hardware customization or provided limited functionality with static overlays. In addition, the investigation of tactile solutions for large touchscreens may not address the challenges on mobile devices. We therefore present Interactiles, a low-cost, portable, and unpowered system that enhances tactile interaction on Android touchscreen phones. Interactiles consists of 3D-printed hardware interfaces and software that maps interaction with that hardware to manipulation of a mobile app. The system is compatible with the built-in screen reader without requiring modification of existing mobile apps. We describe the design and implementation of Interactiles, and we evaluate its improvement in task performance and the user experience it enables with people who are blind or have low vision.