Healthcare digitalization presents transformative opportunities, enabling enhanced patient care, operational efficiency, and cost reductions. However, this rapid adoption of technologies such as electronic health records, artificial intelligence, and telemedicine, also generates complex ethical and operational dilemmas. This study builds on the concept of digital responsibility, emphasizing the ethical management of digital innovations to maximize societal benefits while safeguarding patient rights, privacy, and equitable access. Guided by paradox theory, we explore how healthcare organizations navigate competing demands, focusing on three core tensions: the innovation-stability paradox, the accessibility-privacy paradox, and the ethics-agility paradox. Through qualitative research, we conducted 16 in-depth interviews with decision-makers in the Swiss healthcare sector, supplemented by document analysis. Our findings reveal the challenges in balancing the drive for technological advancement with the need for operational stability, protecting sensitive data while ensuring accessibility, and aligning ethical oversight with rapid innovation. Discussing our preliminary results will add to the discourse on responsible digital innovation in healthcare by providing empirically grounded, actionable insights for managing ethical and operational complexities. With a finalized analysis, we hope to generalize findings across diverse healthcare contexts and refine strategies for integrating ethics into healthcare digital transformation.