The contact between two layers of double-chained C-18 surfactants adsorbed on silica has been investigated. Using a custom-made surface forces apparatus with high stiffness, we have studied the process of (1) compression and collapse of the layers and (2) surface separation after layer collapse. A continuum mechanics model accounts for the compression and collapse of the surfactant layers. The layer compressibility and molecular energy of rupture can be inferred directly. When the surfaces are rinsed in deionized water, an intriguing structural force is observed: the resulting attractive interaction induces the diffusion of surfactant to the contact area, with the gradual buildup of a capillary bridge of the pure smectic phase of the surfactant. Models are proposed to analyze the force profile.