The grand canonical Monte Carlo technique is used to simulate the pressure-distance dependence for supported dilauroylphosphatidylethanolamine (DLPE) membranes. The intra- and intermolecular interactions in the system are described with a combination of an AMBER-based force field for DLPE and a TIP4P model for water. To improve the balance between the pair interactions of like and unlike molecules, the water-lipid interaction potentials are scaled to reproduce the hydration level and intermembrane separation at full hydration. It is found that the short-range water-mediated repulsion originates from the hydration component of the intermembrane pressure, whereas the direct interaction between the membranes remains attractive throughout the pressure range studied (0-5 kbar).