•Polynomial and interpolation models allow for interface displacement reconstruction.•Complex polynomial models outperform the rigid model using the same indicators.•The proposed approaches can be combined for an extended capability.•The method is numerically validated in the context of substructuring. Frequency response functions (FRF) are valuable structure characterizations that are used for the study of noise and vibration, load identification, modal analysis or model updating. They are usually estimated as mobilities by exciting the structure and measuring the normalized response for each frequency. However, rotational degrees of freedom (DOF) are typically difficult or impossible to measure directly. Previous studies have shown that rotational DOFs can be critical for the successful application of different techniques, such as dynamic substructuring. Consequently, different approaches have been proposed to take them into account, such as the finite differences method. Frequency Based Substructuring (FBS) is a dynamic substructuring technique that allows for the coupling of the frequency response functions of separate subsystems in order to synthesize the coupled system's FRFs without the physical assembly. This technique can be sensitive to inconsistencies between the substructures or incomplete information in the interface characterization. The inclusion of rotational degrees of freedom in the FRFs of the interfaces for the application of substructuring has been extensively discussed in literature, but there are still some limitations in frequency due to the assumptions that are required, especially the rigidity assumption of the interfaces. The goal of this paper is to present an experimental approach to relax the rigidity assumption and increase the complexity of the force and displacement field characterization of interfaces. This would extend the value of the estimated FRFs to higher frequency ranges, in which the local deformations start to have an important effect. To particularize the general approach, different possible models are proposed and discussed, highlighting their benefits and disadvantages. Some of these models are validated numerically and experimentally. Finally, the performance of the approach for substructuring applications is also analyzed on a numerical model.