Material imperfections negatively affect the properties of composites. Measurements show that these imperfections are spatially correlated. However, structural reliability analyses often neglect the auto- and intercorrelation of material variability. It remains unclear whether this simplification is justified or not. Therefore, this paper utilizes a numerically efficient multiscale framework to capture the composite spatial variability of fibre volume fraction, fibre misalignment and fibre strength at the micro- and mesoscale. At the structural macroscale, intercorrelation between homogenized apparent material properties is modelled using state-of-the-art vine copulas. The effect of auto- and intercorrelation on the tensile strength of a unidirectional coupon is studied first. Next, their effect on the burst pressure of a composite pressure vessel is investigated to serve as a structural example. The sensitivity analysis elucidates the importance of including material inter- and autocorrelation during the propagation of composite variability.