In this paper, a carbon-fibre/epoxy (CF) composite with nacre-inspired tiled micro-structure is designed and synthesised. The aim is to investigate the interaction between the CF discontinuous micro-structure and continuous glass-fibre/epoxy (GF) layers, which are intended to act as crack stoppers, similarly to the organic interlayers that separate layers of ceramic tiles in natural nacre. Firstly, we use a GF skin to trigger unstable failure in nacre-like mesolayers, and show how the damage mode in the latter changes from pull-out to brittle fibre fracture due to the interaction with the GF skin. Secondly, we demonstrate how continuous GF interlayers can succeed in arresting unstable crack propagation in the nacre mesolayers. Furthermore, we show that they can also change the morphology of damage in the nacre, promoting a transition from brittle tile fracture to more damage-tolerant tile pull-out.