Accelerated by the COVID-19 pandemic, anthropomorphic service robots are continuously penetrating various domains of our daily lives. With this development, the urge for an interdisciplinary approach to responsibly design human-robot interaction (HRI), with particular attention to human dignity, privacy, compliance, and transparency, increases. This paper contributes to design science, in developing a new artifact, i.e., an interdisciplinary framework for designing responsible HRI with anthropomorphic service robots, which covers the three design science research cycles. Furthermore, we propose a multi-method approach by applying this interdisciplinary framework. Thereby, our finding offer implications for designing HRI in a responsible manner.