Traditional damping treatments are usually applied to the vibrating structure by means of adhesive layers. Environmental parameters, such as frequencies of excitation, may influence the behaviour of the bonding layer and modify the damping efficiency of the treatment. Therefore it is desired to take into account the viscoelastic behaviour of the adhesive layer in the finite element model. The goal of this work is to present a procedure to characterise and model the adhesive layer. To that purpose, an experimental-numerical method for inverse characterisation of the frequency dependent properties of the adhesive layer is applied. The proposed inverse approach is based on a four-parameter fractional derivative model whose parameters are identified by minimising the difference between the simulated and the measured dynamic response of a multi-layered structure assembled by bonding. In the finite element model used for the optimisation, the adhesive layer is modelled by interface finite elements. The influence of the adhesive layer on the efficiency of a damping treatment is evidenced by performing dynamic testing on a sandwich structure with a viscoelastic core, assembled by bonding. The proposed approach is applied to the characterisation of a pressure-sensitive adhesive.