This paper introduces the Human-AI Governance (HAIG) framework, contributing to the AI Governance (AIG) field by foregrounding the relational dynamics between human and AI actors rather than treating AI systems as objects of governance alone. Current categorical frameworks (e.g., human-in-the-loop models) inadequately capture how AI systems evolve from tools to partners, particularly as foundation models demonstrate emergent capabilities and multi-agent systems exhibit autonomous goal-setting behaviours. As systems are deployed across contexts, agency redistributes in complex patterns that are better represented as positions along continua rather than discrete categories. The HAIG framework operates across three levels: dimensions (Decision Authority, Process Autonomy, and Accountability Configuration), continua (continuous positional spectra along each dimension), and thresholds (critical points along the continua where governance requirements shift qualitatively). The framework's dimensional architecture is level-agnostic, applicable from individual deployment decisions and organisational governance through to sectorial comparison and national and international regulatory design. Unlike risk-based or principle-based approaches that treat governance primarily as a constraint on AI deployment, HAIG adopts a trust-utility orientation - reframing governance as the condition under which human-AI collaboration can realise its potential, calibrating oversight to specific relational contexts rather than predetermined categories. Case studies in healthcare and European regulation demonstrate how HAIG complements existing frameworks while offering a foundation for adaptive regulatory design that anticipates governance challenges before they emerge.