It is empirically known that anionic polyelectrolytes present in cystic fibrosis (CF) airways due to bacterial infection significantly decrease the activity of cationic antimicrobials via electrostatic binding. In this work, we use synchrotron small-angle X-ray scattering to investigate the interaction between tobramycin, an aminoglycoside antibiotic commonly administered to CF patients via inhalation, with DNA, which is found in high concentrations in the CF airway. We find that interactions between DNA and tobramycin are significantly modified by the presence of mixtures of amphiphilic molecules. We measure a hierarchy of self-assembled structures formed between tobramycin, DNA, and the amphiphile mixtures and show how interactions between these components can be controlled. Results indicate that mixtures of cationic and negative curvature amphiphiles optimized for DNA binding via charge matching and curvature matching can competitively displace bound tobramycin from DNA and thereby drastically suppress tobramycin-DNA binding and resultant antimicrobial inactivation. Growth inhibition assays confirm the increased activity of tobramycin in the presence of DNA with the addition of the amphiphiles. These results suggest that optimized cationic amphiphile solutions have the potential to enhance antimicrobial function in highly infected environments that contain increased concentrations of anionic inflammatory polymers.