Mitochondrial membranes are unique in many ways. Unlike other cellular membranes, they are comprised of two membranes instead of just one, and cardiolipins, one of the abundant lipid species in mitochondrial membranes, are not found in significant amounts elsewhere in the cell. Among other aspects, the exceptional nature of cardiolipins is characterized by their small charged head group connected to typically four hydrocarbon chains. In this work, we present atomic-scale molecular dynamics simulations of the inner mitochondrial membrane modeled as a mixture of cardiolipins (CLs), phosphatidylcholines (PCs), and phosphatidylethanolamines (PEs). For comparison, we also consider pure one-component bilayers and mixed PC-PE, PC-CL, and PE-CL membranes. We find that the influence of CLs on membrane properties depends strongly on membrane composition. This is highlighted by studies of the stability of CL-containing membranes, which indicate that the interactions of CL in ternary lipid bilayers cannot be deduced from the corresponding ones in binary membranes. Moreover, while the membrane properties in the hydrocarbon region are only weakly affected by CLs, the changes at the membrane-water interface turn out to be prominent. The effects at the interface are most evident in membrane properties related to hydrogen bonding and the binding phenomena associated with electrostatic interactions.