Hydrogen bonding is one of the most widely used noncovalent interactions for assembling multicomponent materials. Specifically, hydrogen bonds involving carboxylic acids and pyridines are exceptionally reliable, and although frequently utilized, the influence of COO-H···N and C-H···O hydrogen bonds on thermal expansion (TE) behavior is underexplored. Here, we describe a series of isostructural cocrystals wherein the components self-assemble into two-dimensional (2D) hydrogen-bonded sheets through a combination of COO-H···N and C-H···O hydrogen bonds. We describe the contribution of these two classic interactions to the TE behavior of the cocrystals. Specifically, two cocrystals exhibit 2D zero TE, and two cocrystals exhibit one-dimensional zero TE. This rare behavior results from the interactions sustaining the 2D hydrogen-bonded sheets, which work in tandem to control TE within the sheets.