Bacterial biofilm infections, particularly those of Pseudomonas aeruginosa (PA), have high rates of antimicrobial tolerance and are commonly found in chronic wound and cystic fibrosis lung infections. Combination therapeutics that act synergistically can overcome antimicrobial tolerance; however, the delivery of multiple therapeutics at relevant dosages remains a challenge. We therefore developed a nanoscale drug carrier for antimicrobial codelivery by combining approaches from polyelectrolyte nanocomplex (NC) formation and layer-by-layer electrostatic self-assembly. This strategy led to NC drug carriers loaded with tobramycin antibiotics and antimicrobial silver nanoparticles (AgTob-NCs). AgTob-NCs displayed synergistic enhancements in antimicrobial activity against both planktonic and biofilm PA cultures, with positively charged NCs outperforming negatively charged formulations. NCs were evaluated in mouse models of lung infection, leading to reduced bacterial burden and improved survival outcomes. This approach therefore shows promise for nanoscale therapeutic codelivery to treat recalcitrant bacterial infections.