<div>The automated analysis of digital human communication data often focuses on specific aspects like content or network structure in isolation, while classical communication research stresses the importance of a holistic analysis approach. This work aims to formalize digital communication analysis and investigate how classical results can be leveraged as part of visually interactive systems, which offers new analysis opportunities to allow for less biased, skewed, or incomplete results. For this, we construct a conceptual framework and design space based on the existing research landscape, technical considerations, and communication research that describes the properties, capabilities, and composition of such systems through 30 criteria in four analysis dimensions. We make the case how visual analytics principles are uniquely suited for a more holistic approach by tackling the automation complexity and leverage domain knowledge, paving the way to generate design guidelines for building such approaches. Our framework provides a common language and description of communication analysis systems to support existing research, highlights relevant design areas while promoting and supporting the mutual exchange between researchers. Additionally, our framework identifies existing gaps and highlights opportunities in research areas that are worth investigating further. With this contribution, we pave the path for the formalization of digital communication analysis through visual analytics.</div>