In this paper, we present the results from measurements of forces between macroscopic mica surfaces immersed in an L(3) (sponge) phase. Two different surfactant systems are investigated. As previously reported (Petrov, P.; et al. Langmuir 1994, 10, 988) for the AOT/brine/water L(3) phase, two distinct regions in the force profile are observed : At large separations (40-120 nm), the force is oscillatory due to the structure in the bulk solution. In a confined space, at separations smaller than similar to 30 nm, there is a topological transition to a layered, lamellar-like structure with a force having huge repulsive barriers with a period of 3-3.5 nm, weakly dependent on concentration. The same characteristic forces are observed for an L(3) phase made of C(12)E(5)/hexanol/water. The period of long-range oscillations, scaled by the thickness of the bilayer, is inversely proportional to the surfactant volume fraction and shows a uniform functional dependence for both L(3)-phase systems, in accordance with the general scaling law. Model calculations of the force profile within the flexible surface model reproduce and rationalize all qualitative observations and give a reasonable quantitative estimate of the force. We derive generally applicable conditions for the appearance of a stable lens of lamellar phase between curved surfaces in a bulk L(3) solution and calculate the force explicitly, without invoking the Derjaguin approximation.