Using the surface-force apparatus (SFA), we have made out-of-contact force and in-contact adhesion measurements between composite Langmuir-Blodgett (LB) bilayers. The outer layer is a crystalline monolayer of a novel glycine-containing amphiphile, whose headgroups make a strong, hydrogen-bond-aided adhesion when in normal contact with an identical monolayer. Two different inner layers were studied, with different affinities for the mica substrate. One, a crystalline monolayer of the phospholipid dipalmitoylphosphatidyl-ethanolamine (DPPE), is held onto mica by comparatively weak interactions. Another monolayer, a covalently polymerized network of octadecyltriethoxysilane (OTE), is covalently anchored to plasma-treated mica through the thermal hydrolysis of silanol groups on both substrate and monolayer. We observe that separation of two DPPE/glycine-amphiphile bilayers in hydrogen-bonded contact lends to fracture at the mica/bilayer interface, with a pull-off force of F/R = -75 mN/m. Bonded OTE/glycine-amphiphile bilayers fracture at the OTE/glycine-amphiphile interface, with a pull-off force of F/R = -142 mN/m. These results demonstrate that the mechanisms of LB film fracture cannot be explained considering only the breaking of hydrophobic contacts between neighboring amphiphile tails.