The interaction between crack propagation and interfaces is one of the critical problems in bimaterial systems. In this paper, interfacial and subinterfacial fracture behaviors are simulated to investigate this interaction. The modeling approach for bimaterial structures is first introduced, where the extended bond-based peridynamic model is adopted. Then a convergence study is carried out with a bimaterial plate containing two asymmetric inclusions under tensile load. The comparison with the finite element solution validates the proposed modeling approach. Subsequently, several interfacial and subinterfacial fracture cases are considered to pinpoint the influence of interfaces on crack propagation. The numerical results show that the proposed method can satisfactorily capture the interplay between interfaces and crack propagation. Furthermore, in the subinterfacial fracture case, an equilibrium state of mode-I crack growth is successfully obtained, implying that a specific loading condition can counteract the effect of the interface.