In this work, we report the synthesis of photocurable, ternary polymer networks prepared by incorporating dopamine acrylamide (DAm) into a cross-linked thiol–ene network based on pentaerythritol triallyl ether (APE) and pentaerythritol tetra(3-mercaptopropionate) (PETMP). We systematically evaluate the effect of DAm, in the nonoxidized catechol form, on photopolymerization kinetics and thermal, thermomechanical, and mechanical properties of the modified thiol–ene networks. We show that while DAm only affects photopolymerization kinetics at high concentrations, the presence of the catechol moiety significantly increases the glass transition temperature of the networks across the compositional range (0–50 mol % DAm) due to hydrogen bonding interactions between the catechol and various hydrogen bonding acceptors (ethers, amides, esters) within the network, despite an obvious decrease in cross-link density with increasing concentration of the monofunctional acrylamide. Similarly, trends in the mechanical properties of the DAm–APE–PETMP networks reflect the interplay that exists between competing network design parameters, including the catechol hydrogen bonding interactions and the decrease in cross-link density derived from the use of a monofunctional acrylamide—both of which simultaneously influence network properties. Additionally, we report improved macroscopic adhesion of DAm–APE–PETMP coatings to a range of substrates—including glass, aluminum, steel, and marble—by systematically varying the amount of DAm in the network. Adhesion of the DAm–APE–PETMP coatings were evaluated using two methods, including pull-off and crosshatch adhesion tests.