In this paper, a finite element (FE) modeling method is proposed to predict the structural behaviors of composite members of ultrahigh-performance concrete (UHPC) and normal concrete (NC). This FE modeling method integrates: (i) over-nonlocal gradient-enhanced damage model for UHPC and NC, capable of circumventing strong mesh dependency of the classical continuum damage model and spurious damage growth of the standard gradient-enhanced damage model; and (ii) the irreversible viscosity-regularized cohesive zone formulation to describe UHPC-NC interfacial behaviors. Linearization of relative governing equations is presented and the framework is realized on general FE platform ABAQUS through user subroutines UEL and UMAT. Three UHPC-NC composite specimens were prepared to validate the versatility of the numerical method. Improved slant shear test was accompanied to realistically quantify the UHPC-NC bond strength. The height of UHPC substrate governed the overall behaviors and leaded to complete different failure patterns. It is validated that incorporating the material properties and bond behaviors in this paper predicts the composite specimens' behaviors in an accurate and efficient way.