The cell envelope in Gram-negative bacteria comprises two distinct membranes with a cell wall between them. There has been a growing interest in understanding the mechanical adaptation of this cell envelope to the osmotic pressure (or turgor pressure), which is generated by the difference in the concentration of solutes between the cytoplasm and the external environment. However, it remains unexplored how the cell wall, the inner membrane (IM), and the outer membrane (OM) effectively protect the cell from this pressure by bearing the resulting surface tension, thus preventing the formation of inner membrane bulges, abnormal cell morphology, spheroplasts and cell lysis. In this study, we have used molecular dynamics (MD) simulations combined with experiments to resolve how and to what extent models of the IM, OM, and cell wall respond to changes in surface tension. We calculated the area compressibility modulus of all three components in simulations from tension-area isotherms. Experiments on monolayers mimicking individual leaflets of the IM and OM were also used to characterize their compressibility. While the membranes become softer as they expand, the cell wall exhibits significant strain stiffening at moderate to high tensions. We integrate these results into a model of the cell envelope in which the OM and cell wall share the tension at low turgor pressure (0.3 atm) but the tension in the cell wall dominates at high values (>1 atm).