Urban green infrastructure (UGI) is a prominent concept towards climate adaptation and urban resilience, but is also affected by droughts and heat. Hence, this study aims to advance the multi-assessment of drought and heat risks for UGI through a framework with conceptual and methodological features, paving the way towards knowledge creation and decision support. The framework was systematically developed, starting with defining the situation, analyzing concepts, and finally, constructing the framework. The situation is interpreted as a Coupled Human and Natural System to represent the biophysical and immaterial elements, processes and interrelations. Further, the concepts of risk, UGI and ecosystem services come together in a risk system showing the compound hazards, the exposure, and the cascading vulnerabilities of the UGI. The drought and heat risk assessment framework distinguishes two stages, multi-risk analysis, and multi-criteria risk evaluation. The analysis includes definition and interpretation of the UGI situation under drought and heat conditions, analyzing the hazards, exposure, and vulnerabilities of the system, and translating the risk system into an indicator-based information system. Hereby, the vulnerability analysis of the biophysical UGI aspects comprises the susceptibility and resilience of UGI entities, as well as the degree to which providing ecosystem functions and services can be affected. The multi-criteria risk evaluation covers the assignment of thresholds and weights for indicators, in addition to the aggregation methods. The resulting framework intends to support local actors in the risk assessment of current and future conditions, fostering evidence-based decisions and interventions to deal with risks.