Cellular membranes have a complex phospholipid composition that varies greatly depending on the organism, cell type and function. In spite of this complexity, most structural data available for phospholipid bilayers concern model systems containing only one or two different phospholipids. Here, we examine the effect of cholesterol on the structure of a complex membrane reflecting the lipid composition of mitochondrial membranes, with five different types of headgroups (phosphatidylcholine (PC), phosphatidylethanolamine (PE), phosphatidylinositol (PI), phosphatidylserine (PS) and cardiolipin (CL)) and a variety of hydrocarbon tails. This particular system was chosen because elevated cholesterol contents in mitochondrial membranes have been linked to a breaking down of Bax-mediated membrane permeabilization and resistance to cancer treatments. High resolution electron density profiles were determined by X-ray reflectivity, while the area per phospholipid chain, Apc, and the chain order parameter, SX-ray, were determined by wide-angle X-ray scattering (WAXS). We show that chain order increases upon the addition of cholesterol, resulting in both a thickening of the lipid bilayer and a reduction in the average surface area per phospholipid chain. This effect, well known as cholesterol's condensation effect, is similar, but not as pronounced as for single-component phospholipid membranes. We conclude by discussing the relevance of these findings for the insertion of the pro-apoptotic protein Bax in mitochondrial membranes with elevated cholesterol content.