Critical infrastructures provide essential services for our modern society. Large-scale natural hazards, such as floods or storms, can disrupt multiple critical infrastructures at once. In addition, a localized failure of one service can trigger a cascade of failures of other dependent services. This makes it challenging to anticipate and prepare adequately for direct and indirect consequences of such events. Existing methods that are spatially explicit and consider service dependencies currently lack practicality, as they require large amounts of data. To address this gap, we propose a novel method called DISruptionMap which analyzes complex disruptions to critical infrastructure services. The proposed method combines (i) spatial service models to assess direct service disruptions with (ii) a service dependency model to assess indirect (cascading) service disruptions. A fault tree-based approach is implemented, resulting in a significant decrease in the information required to set up the service dependency model. We demonstrate the effectiveness of our method in a case study examining the impact of an extreme flood on health, transport, and power services in Cologne, Germany.