Cononsolvency occurs if a mixture of two good solvents causes the collapse or demixing of polymers into a polymer-rich phase in a certain range of compositions of these two solvents. The better solvent is usually called the cosolvent, and the other common solvent is called the solvent. An unsolved problem in the understanding of the cononsolvency transition of polymers is the role of various polymer-solvent and cosolvent-solvent interactions. In this work, using a mean-field model, we offer a comprehensive and quantitative theoretical study of the cononsolvency effect of neutral immobilized polymers, in particular, poly(Nisopropylacrylamide) (PNiPAAm) brushes and macrogels. Our model quantitatively describes and predicts the phase-transition behaviors of PNiPAAm brushes and gels in various aqueous alcohol solutions. We demonstrated that in addition to the dominant polymer-cosolvent preferential adsorption and monomer-cosolvent-monomer triple contact (cosolvent-assisted temporary crosslinking effect), a nonideal mixing between the polymer and solvent shifts the collapse transition to the lower-concentration region of the cosolvent, while an increase of the demixing tendency between the cosolvent and solvent reduces the width of the cononsolvency transition. Moreover, weakening of the cononsolvency transition in cosolvent-poor aqueous solutions at high hydrostatic pressure can be explained by the suppression of demixing tendencies between the cosolvent and water, and between polymer and water in the case of PNiPAAm.