Cis-regulatory elements (CREs), such as promoters and enhancers, interact with transcription factors (TFs) to drive gene regulatory programs and contribute to morphological diversity across species. Comparative regulatory genomics, which integrates omic measurements across species, offers a powerful framework for studying the evolution of gene regulation. While multi-omic profiling, combining transcriptomic and epigenomic data, has advanced, computational tools that are both phylogenetically aware and capable of analyzing high-dimensional, cross-species data remain scarce. To address this, we introduce Phylogenetic Dynamic Regulatory Module Networks (P-DRMN), a novel multi-task regression-based algorithm that models dynamic gene module regulatory networks using RNA-seq, ATAC-seq, and ChIP-seq data while incorporating phylogenetic relationships. P-DRMN clusters genes into similarly expressing, discrete gene modules based on expression levels and uses a regression function of upstream CREs to infer species-specific module-TF regulatory programs. We applied P-DRMN to aortic endothelial cell data, including gene expression, promoter/motif accessibility, and five histone modifications (H3K27ac, H3K36me3, H3K4me3, H3K4me2, H3K27me3), from five mammals (human, rat, cow, pig, and dog). P-DRMN inferred 19-65% conservation of gene modules across species, with high- and low-expression modules being the most conserved and diverged, respectively. We identified 103 transitioning gene sets with species- or clade-specific expression patterns, many regulated by distinct TFs and chromatin marks, for example, CTCF in human-specific high-expression modules, and SHOX2, H3K27me3, and H3K4me3 in pig/cow-specific high-expression modules. These results demonstrate how CREs and chromatin states shape species-specific gene expression. Overall, P-DRMN provides a powerful framework for integrating multi-omics data to study the evolutionary dynamics of gene regulation.