In the atomic force microscopy (AFM) investigation of soft polymers and liquids, the tip–sample interaction is dominated by long-range van der Waals forces, capillary forces and adhesion. Furthermore, the tip can indent several tens of nanometres into the surface, and it can pull off a polymer filament from the surface. Therefore, measuring the unperturbed shape of a polymeric fluid can be challenging. Here, we study the tip–sample interaction with polystyrene droplets swollen in chloroform vapour, where we can utilize the solvent vapour concentration to adjust the specimen's mechanical properties from a stiff solid to a fluid film. With the same AFM tip, we use two different AFM force spectroscopy methods to measure three-dimensional (3D) depth profiles of the tip–sample interaction: force–distance (FD) curves and amplitude–phase–distance (APD) curves. The 3D depth profiles reconstructed from FD and APD measurements provide detailed insight into the tip–sample interaction mechanism for a fluid polymer solution. The fluid's intrinsic relaxation time, which we measure with an AFM-based step-strain experiment, is essential for understanding the tip–sample interaction mechanism. Furthermore, measuring 3D depth profiles and using APD data to reconstruct the unperturbed surface comprise a versatile methodology for obtaining accurate dimensional measurements of fluid and gel-like objects on the nanometre scale.