Triple-negative breast cancer (TNBC), especially the subset with a basal phenotype, represents the most aggressive subtype of breast cancer. Unlike other solid tumors, TNBCs harbor a low number of driver mutations. Conversely, we and others have demonstrated a significant impact of epigenetic alterations, including DNA methylation and histone post-translational modifications, affecting TNBCs. Due to the promising results in pre-clinical studies, histone deacetylase inhibitors (HDACi) are currently being tested in several clinical trials for breast cancer and other solid tumors. However, the genome-wide epigenetic and transcriptomic implications of HDAC inhibition are still poorly understood. Here, we provide detailed information about the design of a multi-platform dataset that describes the epigenomic and transcriptomic effects of HDACi. This dataset includes genome-wide chromatin accessibility (assessed by ATAC-Sequencing), DNA methylation (assessed by Illumina HM450K BeadChip) and gene expression (assessed by RNA-Sequencing) analyses before and after HDACi treatment of HCC1806 and MDA-MB-231, two human TNBC cell lines with basal-like phenotype.