Natural fibre-reinforced composites (NFRC) are attracting more and more attention as they are low-cost, environmentally friendly, and lightweight alternatives compared to composites made of synthetic fibres. Composites made of flax/epoxy are one of the typical NFRCs which may have wide applications such as automotive, electronics, and sporting goods. To increase the mechanical and hygrothermal performance of the flax/epoxy laminate, layers of glass/epoxy are used to create a glass/flax composite. However, the conventional drilling method of this glass/flax laminate results in poor hole quality and the damage mechanisms in drilling have yet to be fully understood. Hence, this study systematically investigated the hole quality and drilling damage mechanisms via various drilling processes, including conventional dry drilling with and without backup support, cryogenic drilling, and hybrid drilling combining both the backup support and the cryogenic conditions. The thrust force, delamination, surface roughness and topography of the hole were investigated. Moreover, Micro-computed tomography (Micro-CT) has been utilized for the detection of internal defects. Delamination was systematically classified and analysed according to their shape and distribution. Furthermore, this investigation precisely located the depth-wise position of delamination. Comparative analyses of various drilling conditions revealed that hybrid drilling surpasses alternative methods in reduced delamination and improved surface roughness.