Supramolecular carriers such as micelles can be used to noncovalently bind drug molecules for pharmaceutical applications. However, these carriers can fundamentally affect diffusion-based drug transport due to host-guest coupled diffusion. We report a ternary interdiffusion study on an ionic drug in aqueous micellar solutions. Specifically, high-precision Rayleigh interferometry was used to determine the four multicomponent diffusion coefficients for the potassium naproxenate-tyloxapol-water ternary system at 25 degrees C and pH 7. In addition, we have measured drug solubility as a function of tyloxapol concentration. These measurements were used to characterize drug-surfactant thermodynamic interactions using the two-phase partitioning model. Furthermore, we propose a novel model on host-guest coupled diffusion that includes counterions. We show that quantitative agreement between model and experimental diffusion results can be achieved if the effect of micelle solvation on transport parameters is included in the model. This work represents an essential addition to our previous diffusion study on a nonionic drug and provides guidance for the development of accurate models of drug diffusion-based controlled release in the presence of nanocarriers.