A novel approach to analyze the force response of multiple polymer strands, which are bridged between two surfaces, is proposed. The response of single polymer strands is experimentally accessible by measuring the force upon separation of two polymer-coated surfaces with the atomic force microscope. Our approach is based on the decomposition of the stretching and desorption sequence into contributions of independently bridged chains and of the elimination of loops formed on the opposite surface during contact. This approach was applied to investigate the bridging adhesion of surfaces coated with poly(vinylamine) (PVA). The force response of single PVA molecules was described on the basis of a recently proposed model, which accounts for the discrete chain character of the polymer at higher extension forces. As exemplary results, we determined the length distributions of the individual chains and the loop number distribution of these bridging chains on the polyelectrolyte-coated surfaces. The former were compared with scaling theories of polymer adsorption.