Abstract Safe, economic development of subsurface hydrocarbon resources, as well as emerging hydrogen or CO2 storage projects, relies on accurate characterization of reservoir fractures and faults. The discrete fracture model (DFM) captures low-conductivity barrier faults with high fidelity but becomes computationally expensive for many highly conductive fractures, whereas the embedded discrete fracture model (EDFM) is efficient for conductive fractures yet struggles with low-conductivity features. To reconcile these limitations, this work introduces a tetrahedral grid hybrid model in which DFM is applied during preprocessing to honor low-conductivity faults, and EDFM is applied during post-processing to efficiently model high-conductivity fractures. Governing equations are discretized with a finite volume method, and interfacial fluxes are evaluated using the two-point flux approximation (TPFA), maintaining accuracy while improving runtime. Benchmark comparison against projection-based EDFM (pEDFM) confirms that the hybrid scheme reproduces low-conductivity behavior with equal accuracy. A field-scale case that contains 500 natural fractures, 2 faults, and a multistage fractured horizontal well further shows that the different pressure and water saturation near the low permeability fault. These results demonstrate that the proposed method simultaneously captures the coupled influence of high conductivity fractures and low conductivity faults on multiphase flow, providing an efficient and robust tool for complex reservoir simulation.