The screen-printed electrodes have gained increasing importance due to their advantages, such as robustness, portability, and easy handling. The manuscript presents the investigation of the interaction between double-strand deoxyribonucleic acid (dsDNA) and three anthracyclines: epirubicin (EPI), idarubicin (IDA), and doxorubicin (DOX) by differential pulse voltammetry on metal nanoparticles modified by screen-printed electrodes. In order to investigate the interaction, the voltammetric signals of dsDNA electroactive bases were used as an indicator. The effect of various metal nanomaterials on the signals of guanine and adenine was evaluated. Moreover, dsDNA/PtNPs/AgNPs/SPE (platinum nanoparticles/silver nanoparticles/screen-printed electrodes) was designed for anthracyclines–dsDNA interaction studies since the layer-by-layer modification strategy of metal nanoparticles increases the surface area. Using the signal of multi-layer calf thymus (ct)-dsDNA, the within-day reproducibility results (RSD%) for guanine and adenine peak currents were found as 0.58% and 0.73%, respectively, and the between-day reproducibility results (RSD%) for guanine and adenine peak currents were found as 1.04% and 1.26%, respectively. The effect of binding time and concentration of three anthracyclines on voltammetric signals of dsDNA bases were also evaluated. The response was examined in the range of 0.3–1.3 ppm EPI, 0.1–1.0 ppm IDA and DOX concentration on dsDNA/PtNPs/AgNPs/SPE. Electrochemical studies proposed that the interaction mechanism between three anthracyclines and dsDNA was an intercalation mode.