Discrete fracture and matrix modeling of coupled flow and geomechanics is instrumental for understanding flow in fractured media for various geoengineering applications such as enhanced geothermal energy systems and groundwater remediation. We employ the governing equations for two-phase flow in deformable fractured porous media with a stress-dependent porosity and permeability model of matrix, and variable fracture aperture and the corresponding permeability. A finite element framework is presented, in which fractures are regarded as low-dimensional objects, to discretize the coupled two-phase flow and geomechanics in fractured porous media. A hybrid method, combining discontinuous Galerkin (DG) and continuous Galerkin (CG) finite element methods (FEM), is utilized to solve for the two-phase flow, while the solid deformation is approximated using a discontinuous Galerkin FEM approach. Several benchmark cases are utilized to examine the accuracy of the proposed hybrid DG-CG FEM method. Further validation is performed using more complex, realistic fracture configurations. As the mechanical characteristics of the fracture and the surrounding matrix differ, the simulation results demonstrate that displacement and stress are discontinuous on both sides of the fracture. While the case with low permeability fractures exhibits pressure jump across the fractures, the pressure changes are reasonably smooth for the conduit fractures.