Epidermal growth factor receptor (EGFR) and human epidermal growth factor receptor 3 (HER3) have been investigated as triple-negative breast cancer (TNBC) biomarkers. Reduced EGFR levels can be compensated by increases in HER3; thus, assaying EGFR and HER3 together may improve prognostic value. In a multi-institutional cohort of 510 TNBC patients, we analyzed the impact of HER3, EGFR, or combined HER3-EGFR protein expression in pre-treatment samples on breast cancer-specific and distant metastasis-free survival (BCSS and DMFS, respectively). A subset of 60 TNBC samples were RNA-sequenced using massive parallel sequencing. The combined HER3-EGFR score outperformed individual HER3 and EGFR scores, with high HER3-EGFR score independently predicting worse BCSS (Hazard Ratio [HR] = 2.30, p = 0.006) and DMFS (HR = 1.78, p = 0.041, respectively). TNBCs with high HER3-EGFR scores exhibited significantly suppressed ATM signaling and differential expression of a network predicted to be controlled by low TXN activity, resulting in activation of EGFR, PARP1, and caspases and inhibition of p53 and NFκB. Nuclear PARP1 protein levels were higher in HER3-EGFR-high TNBCs based on immunohistochemistry (p = 0.036). Assessing HER3 and EGFR protein expression in combination may identify which adjuvant chemotherapy-treated TNBC patients have a higher risk of treatment resistance and may benefit from a dual HER3-EGFR inhibitor and a PARP1 inhibitor.