We derive boundary conditions for two-dimensional parallel and non-parallel flows at the interfaceof a homogeneous and isotropic porous medium and an overlying fluid layer by solving a macroscopicclosure problem based on the asymptotic solution to the generalized transport equations (GTE) in theinterfacial region. We obtained jump boundary conditions at the effective sharp surface dividing the ho-mogeneous fluid and porous layers for either the Darcy or the Darcy-Brinkman equations. We discussthe choice of the location of the dividing surface and propose choices which reduce the distance with theGTE solutions. We propose an ad-hoc expression of the permeability distribution within the interfacialregion which enables to preserve the invariance of the fluid-side averaged velocity profile with respectto the size r0 of the averaging volume. Solutions to the GTE, equipped with the proposed permeabilitydistribution, compare favorably to the averaged solutions to the pore-scale simulations (PSS) when theinterfacial thickness ∆ is adjusted to r0 . Numerical tests for parallel and non-parallel flows using the ob-tained jump boundary conditions or the generalized transport equations show excellent agreement withthe GTE solutions, with experiments and pore-scale simulations. The proposed model of mass and mo-mentum transport is predictive, requiring solely information on the bulk porosity and permeability andthe location of the solid matrix of the porous medium. Our results suggest that the Brinkman correctionsmay be avoided if the ratio a = ∆/δB of the thickness of the interfacial region to the Brinkman pene-tration depth δB is large enough, as the Brinkman sub-layer is entirely contained within the interfacialregion in that case. Our results can be easily extended to deal with three-dimensional configurations andanisotropic porous media.