A polymer-based nanocarrier was developed for the co-delivery of epigenetic and chemotherapeutic drugs. The sterically stabilized hybrid micelle system uses micelles composed of D-α-tocopheryl polyethylene glycol 1000 succinate (vitamin E TPGS or TPGS) and 1, 2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[methoxy(polyethylene glycol)-2000] (DSPE-PEG2000). In this study, suberoylanilide hydroxamic acid (SAHA) and paclitaxel were used as model drugs for combination chemotherapy to enhance therapeutic efficiency in targeting mesenchyme-like triple negative breast cancer (TNBC) cells. Combination therapy of paclitaxel and SAHA in a dual drug micelle system, (P + S)_mic, exhibited an IC50 value of 0.52 μg/mL, which is about 5.91-fold more cytotoxic than the mere combination of free drugs (P + S). Furthermore, the (P + S)_mic formulation was far more effective at inhibiting cell migration by more than 3.4-fold than the control. Thus, our findings show that the co-delivery of these drugs using the micelle system greatly enhances their therapeutic effect at a lower dosage, thereby minimizing toxicity. In addition, this formulation is proved to be remarkably effective in preventing cell migration at low dosage.