While Human-Computer Interaction (HCI) has successfully contributed to innovation, HCI education has made only moderate efforts to include innovation as part of the curriculum. In this paper, therefore, we propose a service-dominant logic-informed framework for teaching innovation in the context of HCI education. Our approach combines service-dominant logic from the field of marketing with experiential and constructivist learning, leveraging value co-creation as the primary method of connecting diverse actors within the service ecology. This aligns with the current conceptualization of central university activities as a triad of research, education, and entrepreneurship. The paper illustrates our framework with experiences from a project-based, bachelor's-level HCI course in the computer science department and shows how value co-creation brings a new dimension to HCI education. The proposed framework and our experience described herein can be useful for teachers designing and improving project-based HCI courses.