Chemotherapy–phototherapy (CTPT) combination drugs co-loaded by targeted DNA nanostructures can achieve controlled drug delivery, reduce toxic side effects and overcome multidrug resistance. Herein, we constructed and characterized a DNA tetrahedral nanostructure (MUC1-TD) linked with the targeting aptamer MUC1. The interaction of daunorubicin (DAU)/acridine orange (AO) alone and in combination with MUC1-TD and the influence of the interaction on the cytotoxicity of the drugs were evaluated. Potassium ferrocyanide quenching analysis and DNA melting temperature assays were used to demonstrate the intercalative binding of DAU/AO to MUC1-TD. The interactions of DAU and/or AO with MUC1-TD were analyzed by fluorescence spectroscopy and differential scanning calorimetry. The number of binding sites, binding constant, entropy and enthalpy changes of the binding process were obtained. The binding strength and binding sites of DAU were higher than those of AO. The presence of AO in the ternary system weakened the binding of DAU to MUC1-TD. In vitro cytotoxicity studies demonstrated that the loading of MUC1-TD augmented the inhibitory effects of DAU and AO and the synergistic cytotoxic effects of DAU + AO on MCF-7 cells and MCF-7/ADR cells. Cell uptake studies showed that the loading of MUC1-TD was beneficial in promoting the apoptosis of MCF-7/ADR cells due to its enhanced targeting to the nucleus. This study has important guiding significance for the combined application of DAU and AO co-loaded by DNA nanostructures to overcome multidrug resistance.