A 1-D Canopy Interface Model (CIM) was developed in order to better simulate the effect of urban obstacles on the atmosphere in the boundary layer. The model solves the Navier-Stokes equations on a high-resolved gridded vertical column. The effect of the surface is simulated testing a set of theories and urban parameterizations. The final proposition guarantees its coherence with past theories in any atmospheric stability and terrain configuration. Obstacle characteristics are computed using surface and volume porosities in each cell of the model domain. These porosities are used to weight several terms in the Navier-Stokes equations. A 1.5-order turbulence closure is used in order to compute the turbulent coefficients with the TKE. The mixing length takes into account the density of the obstacles and their height. The turbulent scheme is designed in order to keep CIM coherent with the Prandtl theory in neutral atmospheric conditions and with the MOST in stratified atmospheric stability when CIM is used over plane surfaces. The modifications brought to the main governing equations are discussed following theoretical analysis and experiences with CIM, simulating the averaged meteorological variables (wind speed, turbulent kinetic energy (TKE), temperature and humidity). Simulations are compared with analytical solutions, when possible, and also simulations issued from a computational fluid dynamics (CFD) model. The results show how constant values, usually prescribed, can be theoretically estimated and how the buoyancy term of the turbulent kinetic energy balance equation should be adjusted accordingly. After modifications, it is shown that CIM is coherent with past propositions in any case of atmospheric stabilities over plane surfaces. The use of CIM in presence of obstacles is based on the extension of the 1.5 order turbulence closure to compute the turbulent coefficients with the TKE. CIM shows simulations in good agreement with the CFD simulations in the presence of obstacles. It is able to reproduce an inertial sub-layer as described by the Prandlt and constant-flux layer theory above a displacement height over a homogeneous canopy.