Natural language comprehension is a complex task that relies on coordinated activity across a network of cortical regions. In this study, we propose that regions of the language network are coupled to one another through subspaces of shared linguistic features. To test this idea, we developed a model-based connectivity framework to quantify stimulus-driven, feature-specific functional connectivity between language areas during natural language comprehension. Using fMRI data acquired while subjects listened to spoken narratives, we tested three types of features extracted from a unified neural network model for speech and language: low-level acoustic embeddings, mid-level speech embeddings, and high-level language embeddings. Our modeling framework enabled us to quantify the stimulus features that drive connectivity between regions: early auditory areas were coupled to intermediate language areas via lower-level acoustic and speech features; in contrast, higher-order language and default-mode regions were predominantly coupled through more abstract language features. We observed a clear progression of feature-specific connectivity from early auditory to lateral temporal areas, advancing from acoustic connectivity to speech- and finally to language-driven connectivity. These findings suggest that regions of the language network are coupled through feature-specific communication channels to facilitate efficient and context-sensitive language processing.