The grand canonical Monte Carlo method is used to study a binary mixture of Lennard-Jones atoms confined to a corrugated slit micropore which is in thermodynamic equilibrium with its bulk phase counterpart. The micropore has atomically structured walls; one of the which possesses nanoscale structure in the form of rectilinear grooves (corrugation). The grooved surface divides the confined fluid him into two strip shaped regions, that inside and that outside the grooves. Transverse solidlike order in the him gives rise to shear stress. Transverse order coupled with packing restrictions give rise to a difference between the pore and bulk fluid mixture compositions. Solidlike order may appear;within the grooves only, outside the grooves only, or in both regions simultaneously. As the relative alignment of the walls is shifted the pore fluid undergoes freeze-thaw cycles in one or both regions with associated changes in the shear stress and pore fluid composition. The degree of transverse order in the film is less than would be expected in a pure Lennard-Jones film and fluid-solid phase transitions are gradual as opposed to sudden as seen in pure Lennard-Jones films. The magnitude of the shear stress is greatest when a fluid-solid phase transition occurs in both regions of the pore.