The effective delivery of pharmaceuticals to the respiratory tract is significantly influenced by the three-dimensional covalent network structure of mucus and the motility of cilia within the airway surface liquid (ASL). This study investigates the dissolution and absorption of three distinct drugs-Salbutamol sulfate (SAL), Tiotropium bromide (TIO), and Rifampicin (RIF)-in the ASL, focusing on individual particles of each drug with an initial diameter of 5 µm. A three-dimensional numerical model that characterizes mucus as a nonlinear viscoelastic fluid was employed for this analysis. To discretize and solve the time-dependent governing equations of fluid flow, along with the diffusion-convection equation for mass transfer, a hybrid immersed boundary-finite difference projection method was utilized within the segment of the tracheal ASL on a staggered grid. The results elucidate the effects of drug solubility and the Ciliary Attachment Ratio (CAR) on the distribution of drug concentration within the ASL. Enhanced drug solubility significantly improves both dissolution and concentration within the ASL, particularly at lower solubility levels. Furthermore, it was determined that the CAR has a substantial effect on drug deposition, with higher solubility leading to increased attachment to cilia rather than direct deposition on the epithelial surface. Analysis of deposition time reveals that the rapid transport of drugs to the epithelium is primarily influenced by the drug's diffusion coefficient. However, the total drug deposition time is significantly affected by both drug solubility and its diffusion coefficient. These findings underscore the necessity of understanding these interactions to optimize drug delivery in respiratory therapies.