To macroscopically describe two-phase flows in porous media, we need accurate modeling of the drag forces between the two fluids and the solid phase. In low-permeability porous media, where capillarity is often dominant, momentum exchange is often neglected and the fluid–fluid drag force is treated as part of the drag between fluids and solid in the momentum transport equation. Two-phase flows in highly permeable porous media, however, are often characterized by a larger interface area between the two fluids and by thin films developing. In such cases, the fluid–fluid drag may play an important role and require a specific description in the momentum transport equations. Here, we use computational methods to study immiscible cocurrent two-phase flows in a microfluidic device made of an array of cylinders squeezed between two plates in a Hele-Shaw cell. The key idea is to solve 2D Stokes–Darcy equations integrated over the height of the cell, allowing us to explore different permeability ranges by changing the gap between the plates while keeping the in-plane 2D geometry in the cell unchanged. We use this approach to ask whether the fluid–fluid drag forces affect the pressure drop and how the permeability modifies the relative importance of the drag forces. We find different behaviors depending on the gap thickness, but the fluid–fluid drag plays a significant role in all cases.