Spatial heterogeneity of adhesion properties is known to result in bridging during debonding of secondary bonded composite joints. The ligaments that bridge both substrates have crack-arrest features and thus significantly enhance the fracture resistance of joints. We have investigated the effect of randomly distributed adhesion properties between the adhesive layer and each composite substrate in previous works; however, the spatial correlation of adhesion heterogeneity within or between the substrates and how it effects the failure of secondary bonded composites is still poorly understood. In this current work, we assume that the spatial heterogeneity of adhesion follows a log-normal distribution. The Napierian logarithm of interface toughness Gc and separating strength S can thus be described by a Gaussian Process. We investigate in detail the effect of spatial correlation both within each substrate and between opposite substrates. Finally, we predict the crack resistance of such joints with adhesives of different mechanical properties. We find that the failure strain of adhesives is important through varying the elongation of ligaments and thus the associated extra dissipated energy. This work represents the first critical step for designing tougher secondary bonded composite joints by triggering and controlling adhesive ligament bridging.