Laminar ceramic composites have been fabricated with thin compressive layers, containing a mixture of alumina and mullite, sandwiched between thicker alumina layers. It has previously been shown that a single crack that extends within a thicker alumina layer can be arrested by the compressive layers to produce a threshold strength, i.e., a strength below which the probability of failure is zero. The behavior of multiple cracks within the laminate has been investigated, to observe the mechanisms of crack interaction and measure their influence on the threshold strength. It was found that when the cracks in adjacent thick layers were offset by a distance less than the thickness of two thick layers, the cracks would interact and decrease the threshold strength. The number of interacting cracks, their orientation, and location can also have an effect on the threshold strength.