We have investigated the interaction between bilayer membranes on the basis of the self-consistent-anisotropic-field (SCAF) theory. The method is applied to dimyristoylphosphatidylcholine (DMPC) lamellae in the presence and in the absence of additives, with and without applied lateral tension, and as a function of the ionic strength in solution. The interaction curve between free-standing DMPC membranes is nonmonotonous. Two repulsive regions, one of electrostatic and one of steric origin, bracket an entropic attraction range. We show that this attraction is enhanced by applying a lateral stress to the membranes. The minimum in the interaction curve is found only at not too high ionic strength. The attraction is caused by an alteration of the head-group conformations when the two bilayers come in close contact. In isolated films, the head groups have a conformation parallel to the membrane surface, but on close approach they cross the gap between the membranes intercalating the head groups of the other membrane. In this way they gain conformational entropy, and therefore the free energy of interaction is negative. We show that upon the addition of alcohols (additive : DMPC = 1:5 volume fraction) the interaction curves remain virtually unaltered. The interaction curves are qualitatively different for DMPC bilayers to which positively or negatively charged surfactants are added; these layers become fully repulsive. For cationic surfactants the repulsion range is shifted to larger separations than for anionic surfactants. This behavior is caused by the pronounced effect of ionic surfactants on the orientation of the head groups of DMPC membranes. For negatively charged surfactants the head group is pulled inward toward the membrane interior, whereas the opposite occurs in the presence of the positively charged additive. These results are in line with NMR experiments found in the literature.