The interactions between polymer molecules in solution are strongly affected by the way that the constituent polymers interact with the solvent. In this work, we use a mixed solvent system (dimethyl sulfoxide and ethylene glycol) to tailor the strength of the hydrogen-bonding interactions between partially quaternized poly(4-vinylpyridine) [QVP] and poly(methacrylic acid) [PMAA]. The charge introduced by the quaternization reaction enables homogeneous solutions to be formed over a large concentration range, even in the presence of attractive hydrogen-bonding interactions between the proton-donating PMAA and the proton-accepting QVP. The viscoelastic properties of equimolar QVP/PMAA solutions are superposed onto master curves that are well-described by a fractional Maxwell liquid model. This model provides a means for quantifying the dependence of the relaxation times on the solvent composition. These relaxation times increase by a factor of 1000 as the hydrogen-bonding interactions are strengthened by a decrease in the DMSO content of the solvent, within a composition regime where the solutions remain homogeneous. A much stronger effect is obtained when the ethylene glycol is replaced by water.