Transverse failure in composite materials is a mechanism in the ultimate failure of the engineering composite. It is controlled by the strength of the fibre/matrix interface and improvement in the strength of this interface will improve the overall transverse strength. Transverse fibre bundle composites (TFBC) have been tested to failure, where the condition of the composite and the fibre/matrix interface have been modified. Progression to failure has been monitored using acoustic emission with the AE data analysed in a novel way using Weibull statistics. Although Weibull statistics have previously been used to characterise fibre bundle failure, where the concept of weakest link applies, this work extends this approach in an empirical way using an acoustic emission form of Weibull equations. The AE profile, when compared to stress/strain data, showed a "quiet-then-noisy" profile for room cured resin, which changed to "noisy-then-quiet" when the resin was post cured. Kevlar reinforced TFBC showed regular AE from low strains. The pattern of AE changed when specimens had been post cured and when the Kevlar fibres had been subjected to ultrasound treatment. Although individual AE events were highly variable, Weibull analysis of the AE parameters derived from a glass reinforced composite proved highly robust, with the AE ringdown count distributions moving to higher values for the more brittle, stronger post-cured resin. Measuring interfacial failure stress via the onset of AE, suggested the interface was weakened, but in a selective way, which did not necessarily show in the final failure stress of the composite.