We present a model applicable to ultrasound contrast agent bubbles that takes into account the physical properties of a lipid monolayer coating on a gas microbubble. Three parameters describe the properties of the shell: a buckling radius, the compressibility of the shell, and a break-up shell tension. The model presents an original non-linear behavior at large amplitude oscillations, termed compression-only, induced by the buckling of the lipid monolayer. This prediction is validated by experimental recordings with the high-speed camera Brandaris 128, operated at several millions of frames per second. The effect of aging, or the resultant of repeated acoustic pressure pulses on bubbles, is predicted by the model. It corrects a flaw in the shell elasticity term previously used in the dynamical equation for coated bubbles. The break-up is modeled by a critical shell tension above which gas is directly exposed to water.