In recent years, serverless computing, especially Function as a Service (FaaS), is rapidly growing in popularity as a cloud programming model. The serverless computing model provides an intuitive interface for developing cloud-based applications, where the development and deployment of scalable microservices has become easier and cost-effective. An increasing number of batch-processing applications are deployed as pipelines that comprise a sequence of functions that must meet their deadline targets to be practical. In this paper, we present our Hybrid Cloud Scheduler (HCS) for orchestrating the execution of serverless batch-processing pipelines deployed over heterogeneous infrastructures. Our framework enables developers to (i) automatically schedule and execute batch-processing applications in heterogeneous environments such as the private edge and public cloud serverless infrastructures, (ii) benefit from cost reduction through the utilization of their own resources in a private cluster, and (iii) significantly improves the probability of meeting the deadline requirements of their applications. Our experimental evaluation demonstrates the efficiency and benefits of our approach.