Urban green infrastructure (UGI) is a prominent concept toward climate adaptation and urban resilience, but it is also affected by droughts and heat. Hence, this study aims to advance the multi-assessment of drought and heat risks (DHRs) for UGI through the DHR assessment framework with conceptual and methodological features, paving the way toward 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 lead to a risk system showing the compound hazards, the exposure, and the cascading vulnerabilities of the UGI. The DHR assessment framework distinguishes two stages, multi-risk analysis and multi-criteria risk evaluation. The analysis includes the definition and interpretation of the UGI situation under drought and heat conditions, analyzing the hazards, exposures, 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 compound DHRs.