The combined finite-discrete element method has been widely used to simulate the progressive fracturing process in brittle rocks. Most simulators developed in this field utilize the intrinsic cohesive zone model to simulate crack initiation and propagation. Although it is easy to implement, it introduces the artificial compliance problem. Accordingly, the extrinsic cohesive zone model is proposed to address this problem. Nevertheless, it introduces the "time discontinuity" problem, i.e., inconsistent local nodal forces before and after cohesive element insertion due to essentially different constitutive models. This study builds upon our previous node binding scheme to eliminate the time discontinuity problem. We propose an implementation that considers the dynamic equilibrium of nodal forces, calculating internal forces acting on adjacent finite element pairs during elastic deformation. When inserting a cohesive element, we achieve a smooth transition of local nodal forces by equating internal forces with cohesive tractions. The proposed node-binding approach has been verified by benchmarking a series of numerical cases. Results demonstrate that our approach effectively resolves both the artificial compliance issue in the intrinsic cohesive zone model and the time discontinuity problem in the extrinsic cohesive zone model. This approach significantly improves simulation stability and accuracy, and may promote further applications of the finite-discrete element method in rock fracture simulations associated with various geotechnical and mining engineering problems.