Summary: The investigation focuses on the hydrodynamic instability of a fully developed pressure-driven flow within a bidisperse porous medium containing an electrically conducting fluid. The study explores this phenomenon using the Darcy theory for micropores and the Brinkman theory for macropores. The system involves an incompressible fluid under isothermal conditions confined in an infinite channel with a constant pressure gradient along its length. The fluid moves in a laminar fashion along the pressure gradient, resulting in a time-independent parabolic velocity profile. Two Chebyshev collocation techniques are employed to address the eigenvalue system, producing numerical results for evaluating instability. Our findings indicate that enhancing the values of the Hartmann numbers, permeability ratio, porous parameter, and interaction parameter contributes to an enhanced stability of the system. The spectral behavior of eigenvalues in the Orr-Sommerfeld problem for Poiseuille flow demonstrates noteworthy sensitivity, influenced by various factors, including the mathematical characteristics of the problem and the specific numerical techniques employed for approximation.