Accountability relationships in the health sector have been influenced by political shifts towards decentralization of government health structures, and the development of digital public space as a new focus for increasing public accountability. In 2013, Indonesia launched a national online complaint handling system called Online Citizen Aspiration and Complaints Service (LAPOR!). This system provides Indonesians with an online mechanism to request information or submit complaints about any type, or policy-level, of public service provision, including health services. This qualitative case study sought to examine the macro context LAPOR! is operating in alongside an illustration of LAPOR!’s functioning in specific organizations on different policy levels. The aim of the study was to gain an understanding of the perceived role of LAPOR! as an accountability mechanism in the Indonesian health sector. A total of 40 semi-structured interviews in Jakarta, Semarang Central Java, and Medan North Sumatra were held between August 2019 and February 2020. Non-participant observation and document review also contributed. LAPOR! and the complaint handling context were found to be complex and evolving. The findings identified good practices, implementation challenges and unintended consequences to complaint handling in Indonesia. The study also developed and piloted a Complex Accountability Systems Framework to operationalize assessing public accountability using a systems approach. The framework combines political, organizational and social dimensions of accountability with the interactions between policy, accountability mechanism, institutional arrangements and data. This offers a flexible approach to identifying synergies and interactions of the component parts in different contexts, while also accounting for the cross-cutting influences of leadership, multi-level power dynamics, and the complexities inherent in accountability mechanisms in the health sector. The findings from this study and this framework are potentially useful to policymakers in Indonesia, actors in countries seeking to introduce online complaint handling, and researchers of accountability systems in complex settings.