The rupture of a foam bilayer in contact with an insoluble monolayer of the amphiphiles building up the bilayer is considered as resulting from nucleation of nanoscopically small holes in the bilayer. An expression is derived for the dependence of the bilayer lifetime tau on the surface pressure pi(s) in the monolayer. It is found that this dependence has a threshold character : tau decreases sharply with decreasing pi(s) in a narrow pi(s) range, and the bilayer ruptures practically instantaneously below a certain critical surface pressure in the monolayer.