Hypothesis: Under axisymmetric conditions, changes in the thickness of the thin film between a fluid drop and a solid revealed by white light interferometry can provide information about the interaction of the bodies. Thus, in principle one can quantify the force between the surfaces using interferometric information of film thickness profile. This is needed to quantify and analyze drop-solid interactions across complex fluids such as an ionic liquid to independently characterize new surface forces. Experiments: Interferometric fringes were obtained in experiments on the interaction between a mercury drop and mica across a film of room temperature ionic liquid. The data is analyzed using a novel formula giving the total force acting on the drop. The calculations are compared with two other approaches to estimating forces. Qualitative and quantitative differences are discussed. Findings: This is the first report of forces measured between mercury and mica across an ionic liquid. The system is subjected to different applied electric potentials. In each case a long ranged, exponentially decaying repulsive force is found. At small separations, the system becomes unstable and the surfaces jump into contact. The comparison of force calculation methods demonstrates the superiority of the force approach proposed here. (C) 2018 Elsevier Inc. All rights reserved.