Transcription factors bind DNA sequence motif vocabularies in cis-regulatory elements (CREs) to modulate chromatin state and gene expression during cell state transitions. A quantitative understanding of how motif lexicons influence dynamic regulatory activity has been elusive due to the combinatorial nature of the cis-regulatory code. To address this, we undertook multiomic data profiling of chromatin and expression dynamics across epidermal differentiation to identify 40,103 dynamic CREs associated with 3,609 dynamically expressed genes, then applied an interpretable deep-learning framework to model the cis-regulatory logic of chromatin accessibility. This analysis framework identified cooperative DNA sequence rules in dynamic CREs regulating synchronous gene modules with diverse roles in skin differentiation. Massively parallel reporter assay analysis validated temporal dynamics and cooperative cis-regulatory logic. Variants linked to human polygenic skin disease were enriched in these time-dependent combinatorial motif rules. This integrative approach shows the combinatorial cis-regulatory lexicon of epidermal differentiation and represents a general framework for deciphering the organizational principles of the cis-regulatory code of dynamic gene regulation.