The translation of mechanical forces into biochemical signals plays a central role in guiding normal physiological processes during tissue development and homeostasis. Interfering with this process contributes to cardiovascular disease, cancer progression, and inherited disorders. The actin-based cytoskeleton and its associated adherens junctions are well-established contributors to mechanosensing and transduction machinery; however, the role of the desmosome–intermediate filament (DSM–IF) network is poorly understood in this context. Because a force balance among different cytoskeletal systems is important to maintain normal tissue function, knowing the relative contributions of these structurally integrated systems to cell mechanics is critical. Here we modulated the interaction between DSMs and IFs using mutant forms of desmoplakin, the protein bridging these structures. Using micropillar arrays and atomic force microscopy, we demonstrate that strengthening the DSM–IF interaction increases cell–substrate and cell–cell forces and cell stiffness both in cell pairs and sheets of cells. In contrast, disrupting the interaction leads to a decrease in these forces. These alterations in cell mechanics are abrogated when the actin cytoskeleton is dismantled. These data suggest that the tissue-specific variability in DSM–IF network composition provides an opportunity to differentially regulate tissue mechanics by balancing and tuning forces among cytoskeletal systems.