Cells in tissues are mechanically coupled both to the ECM and neighboring cells, but the coordination and interdependency of forces sustained at cell-ECM and cell-cell adhesions are unknown. In this paper, we demonstrate that the endogenous force sustained at the cell-cell contact between a pair of epithelial cells is approximately 100 nN, directed perpendicular to the cell-cell interface and concentrated at the contact edges. This force is stably maintained over time despite significant fluctuations in cell-cell contact length and cell morphology. A direct relationship between the total cellular traction force on the ECM and the endogenous cell-cell force exists, indicating that the cell-cell tension is a constant fraction of the cell-ECM traction. Thus, modulation of ECM properties that impact cell-ECM traction alters cell-cell tension. Finally, we show in a minimal model of a tissue that all cells experience similar forces from the surrounding microenvironment, despite differences in the extent of cell-ECM and cell-cell adhesion. This interdependence of cell-cell and cell-ECM forces has significant implications for the maintenance of the mechanical integrity of tissues, mechanotransduction, and tumor mechanobiology.