The present problem is concerned with the flow of micropolar/Eringen fluid sandwiched between two Newtonian fluid layers through the horizontal porous channel. The flow in both the regions is steady, incompressible and the fluids are immiscible. The flow is driven by a constant pressure gradient and a magnetic field of uniform strength is being applied in the direction perpendicular to the flow. The flow of electrically conducting fluids, in the three regions, is governed by the Brinkman equation with the assumption that the effective viscosity of each fluid is the same as the viscosity of the fluid. No-slip conditions at the end of the plates, continuity of velocity, continuity of shearing stress and constant rotational velocity at the interface have been used as the boundary conditions to get the solution of the problem considered. The numerical values of the solution obtained are used to analyse the effect of various transport parameters, such as permeability of porous region, magnetic number, viscosity ratio etc. on the velocity profile and micro rotational velocity profile graphically. Also, the variations in the flow rate and the wall shear stress, with respect to the governing parameters, are presented in tabular form.