Interfaces within glass targets give rise to variations in the mode of failure of material components. The wide use of such laminates merits further investigation of the failure mechanism. It is already known that when shocked above a threshold of 4GPa, glass fails under compression behind a propagating front following the compression front. Work is presented which indicates how this failure process is altered by bonding together two plates to introduce an interface, rather than leaving a monolithic target. After crossing an internal interface, the failure wave propagates only after a delay in soda-lime glass and the failed strength of the material is increased at the inner interface compared with that at the impact face. Addition of a second interface illustrates these effects.