The demand for hybrid composite materials has been expanding globally in all kinds of mechanical industries. Drilling is one of the basic operations required in manufacturing of various components and choosing optimum parameters of drilling is vital for getting good quality holes. The main objective of our work is to determine the ideal parameters of drilling and tool coatings required to minimize the thrust force and torque in drilling and to maximize the material removal rate (MRR) using Grey–Taguchi technique. Hybrid composite specimen made by reinforcing Al7075 alloy with 4% of aluminum oxide and 2% of boron nitride in stir casting process and drilling was carried out in a sequence at different drilling feed rates (40, 80, and 120 mm/min) and spindle speeds (1,200, 2,400, and 3,600 rpm) in a vertical machining center attached with drill tool dynamometer, using twist drills of diameter 5 mm and point angle 118° made of uncoated carbide, diamond-like carbon (DLC)-coated carbide and high carbon (HC)-coated carbide. The recorded thrust force and torque from the dynamometer and the computed MRRs during each drilling operation are tabulated as per Taguchi’s L27 orthogonal array and the results are analyzed using hybrid Grey–Taguchi technique. In our analysis, the optimum thrust force of 62.12 N and torque of 0.766 Nm were obtained when using a DLC-coated tool at a maximum speed of 3,600 rpm and minimum feed rate of 40 mm/min. An optimum MRR of 178.79 mm3/s was obtained while using DLC coated at a maximum speed of 3,600 rpm and a maximum feed rate of 120 mm/min.