Sheaths are formed around the surfaces of airless bodies, which both collect and emit electrons. Depending on the ratio of the emitted to collected electron fluxes Γ, the sheath potential structure can be quite different. We present the first experimental measurements of all the three types of the sheath potentials: classical, space‐charge‐limited (SCL), and inverse. A solid surface immersed in plasmas emits secondary electrons. The potential structure changes from a monotonic classical to a nonmonotonic SCL sheath as Γ increases. At the critical electron emission with zero electric field at the surface, the sheath potential is determined by the plasma electron temperature, and Γ approaches but remains smaller than 1, in agreement with the theoretical expectation. The nonmonotonic SCL sheath persists steadily for Γ > 1. When the emitted electron density becomes larger than the plasma electron density, a monotonic inverse sheath forms with a positive surface potential relative to the ambient.