This article explores the corporate governance of Hybrid Intelligence (HI). We distinguish two fundamental modes of HI: Division of Labour, where humans and AI each specialise in different tasks, and Hybrid Ensembles, where their independent outputs are aggregated. Building on three complementary governance lenses (organisational, human, and societal), we propose a governance framework that synthesises these two modes and examines them across six dimensions: responsibility, transparency, human agency, fairness, risk, and strategic alignment. While HI promises productivity, efficiency, and resilience gains for organisations, it also raises human concerns about fairness, non-discrimination, autonomy, and job security, as well as societal concerns regarding democratic legitimacy. The framework is illustrated through an empirical production dashboard case, showing how HI governance choices shape accountability, autonomy, and legitimacy in practice. We conclude that HI governance is not about choosing one mode over the other but about dynamically balancing them and thus securing value creation and legitimacy across organisational, human, and societal levels. These insights point to future research and practice, highlighting the need to address the temporal dynamics of shifting human–AI roles and to integrate democratic deliberation into corporate governance processes.