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Scattering scanning near-field optical microscopy (s-SNOM) is a powerful technique for mid-infrared spectroscopy at nanometer length scales. By investigating objects in aqueous environments through ultrathin membranes, s-SNOM has recently been extended toward label-free nanoscopy of the dynamics of living cells and nanoparticles, assessing both the optical and the mechanical interactions between the tip, the membrane and the liquid suspension underneath. Here, the study reports that the tapping AFM tip induces a reversible nanometric deformation of the membrane manifested as either an indentation or protrusion. This mechanism depends on the driving force of the tapping cantilever, which is exploited to minimize topographical deformations of the membrane to improve optical measurements. Furthermore, it is shown that the tapping phase delay between driving signal and tip oscillation is a highly sensitive observable to study the mechanics of adhering objects, exhibiting highest contrast at low tapping amplitudes where the membrane remains nearly flat. Mechanical responses are correlated with simultaneously recorded spectroscopy data to reveal the thickness of nanometric water layers between membrane and adhering objects. Besides a general applicability of depth profiling, the technique holds great promise for studying mechano-active biopolymers and living cells, biomaterials that exhibit complex behaviors when under a mechanical load.