A segmented two-phase flow model is developed to describe immiscible two-phase flow in discrete fracture networks; i.e., there is an abrupt interface separating the two immiscible fluids. The capillary pressure on the fluid material interface and gravity are considered. For two-phase flow in fracture networks it is inevitable to form a mixed fluid in some fracture segments. The mixed fluid is described by a homogeneous model, and parameter γ is introduced as a critical value controlling new fluid formation in mixed fluid. The governing equations for two-phase flow are solved with a developed numerical manifold method (NMM) which is verified using the finite element and analytical methods with two examples. Two-phase flow through a single fracture intersection acting as one of the basic elements for complex fracture networks is then analysed. Different inlet and outlet configurations are considered including one-inlet/two-outlets, two-inlets/one-outlet and one-inlet/multi-outlets. For the second configuration, parametric studies of defined parameter γ and boundary conditions are carried out. In the third configuration, capillary pressure and gravity effects are discussed. The developed NMM is applied to the analysis of two-phase flow in a complicated fracture network showing that it is an efficient method for simulating segmented two-phase flow in fracture networks. Complex two-phase flow characteristics in the fracture networks that cannot be addressed in continuum models, e.g., the change in flow direction and transition from static to flow, are also revealed and analysed.