The shape of a soap bubble placed on a solid surface is familiar to everyone a-thin hemispherical dome that thickens near the solid surface. This structure is stabilized by the balance between the film's elasticity, provided by surfactant molecules, and the pressure inside the bubble. However, there is also a soap film on the flat solid surface that has been mostly ignored in previous studies; its thickness is typically assumed to be constant or varying monotonically. In this letter, for the first time, we show that the thickness of this film is not always monotonic. Depending on the surfactant type, it can exhibit a significant dip, similar to marginal pinching. This finding has a significant influence in numerous applications in which solid/foam interactions are important, such as oil extraction or foam-based drug delivery.