The simulation of fluid flow and mechanical deformation, as well as more complex processes such as hydro-mechanical coupling in fractured porous media, is a fundamental task in computational geosciences. One of the main challenges in simulating fractured media is mesh generation: meshes must conform to intricate networks of fractures embedded in a background domain. This task is generally difficult to automate and can lead to computationally expensive problems. Hybrid-dimensional models are a widely used approach to address these challenges. This modeling technique treats the fractures as separate domains, typically of lower geometrical dimension than the embedding background. While this methodology significantly simplifies mesh generation for fractured media, it introduces additional coupling between the equations governing the fracture domain and those in the background domain. In this work, we propose an alternative modeling technique based on interface problems. This approach eliminates the need for an explicit fracture domain and its coupling with the background, modeling fractures instead as interface conditions. These conditions are derived through a formal integration of the governing equations across the fracture domain. We present a detailed validation of this novel approach, demonstrating its effectiveness in capturing the essential physics of fractured porous media while reducing computational complexity.