The user interfaces (UIs) of interactive systems become increasingly complex since many heterogeneous and dynamically changing contexts of use (platform, user, and environment) have to be supported. Developing UIs for such interactive systems often requires features like UI adaptivity and seamless task-continuity across devices, demanding for sophisticated UI development processes and methods. While existing engineering methods like human-centered design process and model-based UI development approaches serve as a good starting point, an integrated engineering process addressing specific requirements of adaptive UIs supporting task-continuity across different devices is not fully covered. Therefore, we present a model-based engineering approach for building context-adaptive UIs that enable a personalized, flexible and task-continuous usage of cross-channel applications. Our engineering approach supports modeling, transformation and execution of context-adaptive UIs. To show the feasibility of our approach, we present an industrial case study, where we implement context-adaptive UIs for a cross-channel banking application.