Measurements with an atomic force microscope (AFM) offer a direct way to probe elastic properties of lipid bilayer membranes locally: provided the underlying stress-strain relation is known, material parameters such as surface tension or bending rigidity may be deduced. In a recent experiment a pore-spanning membrane was poked with an AFM tip, yielding a linear behavior of the force-indentation curves. A theoretical model for this case is presented here which describes these curves in the framework of Helfrich theory. The linear behavior of the measurements is reproduced if one neglects the influence of adhesion between tip and membrane. Including it via an adhesion balance changes the situation significantly: force-distance curves cease to be linear, hysteresis and nonzero detachment forces can show up. The characteristics of this rich scenario are discussed in detail in this paper.