The serverless computing paradigm brings multiple benefits to application developers who are interested in consuming computing resources as services without the need to manage physical capacities or limits. There are several deployment technologies and languages available suitable for deploying applications to a single cloud provider. However, for multi-cloud application deployments, multiple technologies have to be used and orchestrated. In addition, the event-driven nature of serverless computing imposes further requirements on modeling such application structures in order to automate their deployment. In this paper, we tackle these issues by introducing an event-driven deployment modeling approach using the standard Topology and Orchestration Specification for Cloud Applications (TOSCA) that fully employs the suggested standard lifecycle to provision and manage multi-cloud serverless applications. To show the feasibility of our approach, we extended the existing TOSCA-based ecosystem OpenTOSCA.