To improve biodiversity and human living conditions in the Anthropocene, urban forms must reconcile density with vegetation to meet the dual sustainability-liveability challenge. This paradox poses a dilemma for urban planners and is a critical research issue requiring comprehensive analyses. Multi-family residential housing holds the potential to achieve balanced density-greening, proximity ecosystem services and human-nature connectedness, but meeting such objectives relies on finding balanced morphologies and metrics at an operational scale. Analysing 11,593 plots in the Lyon metropolitan area (France) using a systemic approach, we identified critical tipping points in morphology and greening. Density explained only 6% of Plot Greening, while morphology and landscaping accounted for 94%. We identified an open-space ratio (unbuilt area/floor area) >0.3 as a morphological threshold to achieve sustainable green supply. Operational morphologies balancing density and greening were modelled and illustrated across building heights, providing guidelines for emerging regulatory tools in sustainable urban planning.