Today's distributed computing infrastructures encompass complex workflows for real-time data gathering, transferring, storage, and processing, quickly overwhelming centralized cloud centers. Recently, the computing continuum that federates the Cloud services with emerging Fog and Edge devices represents a relevant alternative for supporting the next-generation data processing workflows. However, eminent challenges in automating data processing across the computing continuum still exist, such as scheduling heterogeneous devices across the Cloud, Fog, and Edge layers.We propose a new scheduling algorithm called C 3 -MATCH, based on matching theory principles, involving two sets of players negotiating different utility functions: 1) workflow microservices prefering computing devices with lower data processing and queuing times; 2) computing continuum devices prefering microservices with corresponding resource requirements and less data transmission time. We evaluate C 3 -MATCH using realworld road sign inspection and sentiment analysis workflows on a federated computing continuum across four Cloud, Fog, and Edge providers. Our combined simulation and real execution results reveal that C 3 -MATCH achieves up to 67% lower completion time than three state-of-the-art methods with 10 ms-1000 ms higher transmission time.