Hydrochlorothiazide (HCT) is a diuretic and a BCS class IV drug with low solubility and low permeability, exhibiting poor oral absorption. The present study attempts to improve the physicochemical properties of the drug using a crystal engineering approach with cocrystals. Such multicomponent crystals of HCT with nicotinic acid (NIC), nicotinamide (NCT), 4-aminobenzoic acid (PABA), succinamide (SAM), and resorcinol (RES) were prepared using liquid-assisted grinding, and their solubilities in pH 7.4 buffer were evaluated. Diffusion and membrane permeability were studied using a Franz diffusion cell. Except for the SAM and NIC cocrystals, all other binary systems exhibited improved solubility. All of the cocrystals showed improved diffusion/membrane permeability compared to that of HCT with the exception of the SAM cocrystal. When the solubility was high, as in the case of PABA, NCT, and RES cocrystals, the flux/permeability dropped slightly. This is in agreement with the expected interplay between solubility and permeability. Improved solubility/permeability is attributed to new drug-coformer interactions. Cocrystals of SAM, however, showed poor solubility and flux. This cocrystal contains a primary sulfonamide dimer synthon similar to that of HCT polymorphs, which may be a reason for its unusual behavior. Hirshfeld surface analysis was carried out in all cases to determine whether a correlation exists between cocrystal permeability and drug-coformer interactions.