In this study, the mechanical properties of grain boundaries (GBs) in planar heterostructures of graphene and hexagonal boron nitride (h-BN) were studied using the molecular dynamics method in combination with the density functional theory and classical disclination theory. The hybrid interface between graphene and h-BN grains was optimally matched by a non-bisector GB composed of pentagon–heptagon defects arranged in a periodic manner. GB was found to be a vulnerable spot to initiate failure under uniaxial tension; moreover, the tensile strength was found to anomalously increase with an increase in the mismatch angle between graphene and h-BN grains, i.e., the density of pentagon–heptagon defects along the GBs. The disclination theory was successfully adopted to predict the stress field caused by lattice mismatch at the GB. Comparison between stress contours of GBs with different mismatch angles demonstrates that the arrangement of 5–7 disclinations along the GB is crucial to the strength, and the stress concentration at the GB decreases with an increase in disclination density; this results in an anomalous increase of strength with an increase in the mismatch angle of grains. Moreover, the thermal transfer efficiency of the hybrid GB was revealed to be dependent not only on the mismatch angle of grains but also on the direction of the thermal flux. Thermal transfer efficiency from graphene to h-BN is higher than that from h-BN to graphene. Detailed analyses for the phonon density of states (PDOS) of GB atoms were carried out for the mismatch angle-dependence of interfacial conductance. Our results provide useful insights for the application of two-dimensional polycrystalline heterostructures in next-generation electronic nanodevices.