Many enterprises are opting for the multi-cloud deployment of their complex workflows to avoid vendor lock-in, ensure high reliability, and achieve cost-effective high performance. However, optimally mapping workflows to the cloud services and instances in a multi-cloud environment has many inherent challenges. Cloud service providers (CSPs) have unique cost models. Moreover, various features offered by the corresponding services from multiple cloud service providers differ significantly. Hence, optimal deployment requires a judicious selection of cloud services and their configurations offered by multiple CSPs. Serverless deployment of workloads in the cloud is emerging as a preferred choice due to its high scalability, and cost-effective pay-per-use cost model. In this work, we present analytical model and simulation-based approaches for estimating the makespan and cost of mapping complex workflows to serverless architecture in a multi-cloud environment. Additionally, the schedules generated using a well-known simulator with a brute-force algorithm and an analytical model are evaluated on real cloud instances. We observe an improvement of 53% in the makespan of the workflow and 30% in the cost of deployment when compared with the worst and intuition-based deployment scheme.