Starting from the microscopic description of the system, we derive a set of macroscopic transport equations for fluid and suspension flow in a parallel-wall channel under Stokes-flow conditions. The transport equations involve a generalized permeability (or mobility) relation that links the suspension-volume and particle fluxes to the macroscopic pressure gradient and lateral force acting on the particles. The matrix of transport coefficients in these equations satisfies the Onsager reciprocal relation. Invoking an analogy between the hydrodynamic and electrostatic problems we propose an approximation for the channel permeability coefficients which is similar to the Clausius--Mossotti approximation for the effective dielectric constant. The transport coefficients are evaluated for fixed and mobile arrays of spherical particles. We find that a densely packed fixed particle array reduces the channel permeability to 1% of the permeability of a particle-free channel. We also discuss application of our macroscopic transport equations to describe the shape evolution and fingering instabilities of flow-driven finite regular particle arrays.