A theory is presented for the proton stretch vibrational frequency nu(AH) for hydrogen (H-) bonded complexes of the acid dissociation type, that is, AH center dot center dot center dot B double left right arrow A(-)center dot center dot center dot HB+ (but without complete proton transfer), in both polar and nonpolar solvents, with special attention given to the variation of nu(AH) with the solvent's dielectric constant epsilon. The theory involves a valence bond (VB) model for the complex's electronic structure, quantization of the complex's proton and H-bond motions, and a solvent coordinate accounting for nonequilibrium solvation. A general prediction is that nu(AH) decreases with increasing epsilon largely due to increased solvent stabilization of the ionic VB structure A(-)center dot center dot center dot HB+ relative to the neutral VB structure AH center dot center dot center dot B. Theoretical nu(AH) versus 1/epsilon slope expressions are derived; these differ for polar and nonpolar solvents and allow analysis of the solvent dependence of nu(AH). The theory predicts that both polar and nonpolar slopes are determined by (i) a structure factor reflecting the complex's size/geometry, (ii) the complex's dipole moment in the ground vibrational state, and (iii) the dipole moment change in the transition, which especially reflects charge transfer and the solution phase proton potential shapes. The experimental proton frequency solvent dependence for several OH center dot center dot center dot O H-bonded complexes is successfully accounted for and analyzed with the theory.