Lamellar phases in oil-water-surfactant mixtures are studied in a slit geometry. Within a lattice vector model we obtain the following results in a mean-field approximation. (i) In the case of swollen phases the lamellae are parallel to the walls for all distances L between them and for all surface-field strengths; the system responds elastically to the external stress. (ii) For shorter periods of the bulk phase (surfactant volume fraction rho (s)approximate to1/3) the lamellae are parallel to hydrophilic, and perpendicular to neutral or very weakly hydrophilic surfaces. For a small range of the surface-fields changes of L lead to a switch from the parallel to the perpendicular orientation, as found previously for confined block copolymers. (iii) For still shorter periods (rho (s)greater than or equal to1/2) the perpendicular orientation is stable up to much higher hydrophilicity of the walls. Changes of L induce the switch between the two orientations for a large range of the surface fields. For rho (s)greater than or equal to1/2 the structure in the slit can no longer be described by one-dimensional density profiles even for the parallel orientation. Structural deformations similar to dislocations lead to an inelastic response to compression or expansion.