Biological adhesion typically occurs through discrete cross bridges between complementary molecules on adjacent membranes. Here we report quantitative measurements of the binding distance between a lipid membrane functionalized with ligands on flexible polymer tether chains and a second membrane bearing complementary receptors using the surface force apparatus technique. The binding distance is shown to increase as a function of polymer tether length. Upon separation, adhesive failure occurs not at the strong ligand-receptor bond but primarily through the mechanical pullout of cross-bridging polymer tethers from the membrane. We summarize these measurements of complementary membrane adhesion dynamics using an energy-state diagram that encompasses the energetics of the polymer tether, ligand-receptor bond strength, and number of cross bridges formed.