The integration of renewable energy sources (RES) is essential for steering our energy systems towards sustainability. This transition, though, coupled with emerging trends such as digitalisation and decentralisation, introduces a number of new challenges and vulnerabilities to our energy infrastructure. To strengthen our energy systems against the uncertainties arising from intermittent RES and decentral organised power grids, battery energy storage systems (BESSs) integrated into sector‐coupling strategies might play a crucial role. Such BESSs can enhance system resilience by providing increased flexibility in the face of disruptive events. Yet, the assessment of their resilience contribution is still a nascent field, particularly within the context of multi‐energy systems. To address this gap, our study presents an assessment scheme utilising the open source energy system model electricity grid optimisation. We apply this scheme to evaluate the impact of sector‐coupled BESS installations with a local district heating network in a mid‐sized German city. Our analysis encompasses various scenarios, considering diverse BESS sizes, quantities, seasonal influences, system scales, siting, and the severity of disruptive events. The principal findings are threefold: for energy systems that exhibit high inherent robustness, such as those with existing adaptive capacities and redundancies, hybrid BESS (hBESS) has a low impact on the resilience against single disruptive events. In contrast, for less prepared systems or during simultaneous events, hBESSs can substantially strengthen the resilience of the energy infrastructure, particularly regarding the ‘security of supply’ and ‘cost efficiency’. For instance, during short‐lasting disruptive events, hBESS can potentially avert up potential power outages from 1.4% to 45% increasing the security of supply. However, the resilient design principle ‘spatial diversity’ could not improve the system’s resilience in all scenarios. This holistic approach is essential for identifying resilient strategies capable of effectively countering unforeseen disruptive events, thereby ensuring the continued stability and sustainability of our energy systems.