<p>The present mathematical study involves the multiphase flow of immiscible couple stress and Newtonian fluids through three coaxial circular tubes in which inner cylinder is an impermeable core and remaining two cylinders are porous. The middle tube allows the flow of couple stress fluid, and outer tube is saturated by Newtonian fluid layer. The proposed model is investigated under an inclined magnetic field on fluid flow to explore the flow field including stresses, flow rate, and hydrodynamic permeability. Limiting cases on couple stress-Newtonian model is implemented to transform this model into Newtonian-Newtonian model. Analytical, numerical and graphical estimates are reported for velocity, stress and hydrodynamic permeability for both models. A comparative study between couple stress-Newtonian and Newtonian-Newtonian models is presented numerically and graphically for various values of flow parameters. At the porous interface, velocity is attaining negative values i.e. reverse flow in couple stress-Newtonian model while fluid velocity is always non-negative in the Newtonian-Newtonian model. Contours of fluid velocity for both models are also sketched under the variation of Reynolds number and Hartmann number, and reported the comparison between them. The blood flow dynamics can be studied using this model, where couple stress fluid represents plasma while Newtonian fluid represents the surrounding layer. The outcome of the present study is that it may also be employed to regulate the transport and dispersion of contaminants, treating soil particles as a solid core, whereas pollutants may exhibit couple stress characteristics due to their chemical complexity, and groundwater behaves as a Newtonian fluid.</p>