In this paper, a novel numerical method for strucural analysis, called the Hybrid Discrete-Finite Element Method (HybriDFEM), is presented. In this method, a structure is modeled as an assembly of rigid blocks in contact. All the deformation is concentrated at the interfaces, which are modeled as series of distributed nonlinear multidirectional springs. The method shares similarities with the Discrete Element Methods (DEM) in its ability to account for contact interfaces and/or block deformability, and with the Applied Element Method (AEM) in the representation of interfaces as a series of normal and shear springs. However, it is close to the FEM in the way it is formulated, which offers the possibility to readily link both methods for potential hybrid applications. This paper focuses on the modeling of continuous and discontinuous frames with the HybriDFEM. It is shown how the model can do so with a nonlinear material model, and considering (or not) nonlinear geometric effects through large nodal displacements. Different nonlinear solution procedures implemented in HybriDFEM are demonstrated, such as load-control and various displacement-controlled methods. This model is able to simulate contacts between rigid or deformable units, an important feature when it comes to the modeling of, e.g., unreinforced masonry structures, with a reasonable computational cost and a formulation that is cast within the framework of the classical FEM.