The coupling between proton binding and conformational degrees of freedom in polyprotic molecules and polyelectrolytes is studied theoretically. Our approach combines the classical rotational isomeric state (RIS) model developed by Flory and the site binding (SB) model used to treat proton binding equilibria. The properties of the resulting SBRIS model, which treats conformational degrees of freedom and proton binding on equal footing, are studied with statistical mechanical techniques. Quantities of interest, such as titration curves, conformational probabilities, or macroscopic binding constants, are expressed as thermal averages and are evaluated by direct enumeration of states or by transfer matrix techniques. We further demonstrate that in the SBRIS model conformational degrees of freedom can be averaged out, leading to the contracted description within the SB model. In most cases, this contraction leads to higher order interactions, which may not be present at the SBRIS level (e.g., triplet interactions). Several examples are discussed to illustrate the concepts developed. The case of succinic acid exemplifies the situation in its simplest form. The model can further rationalize the very different titration behavior of poly(acrylic acid) (PAA) and poly(methacrylic acid) (PMAA). In particular, the characteristic "jump" in the titration curve of PMAA is described quantitatively and is interpreted in terms of a conformational transition.