Drilling-induced damage in fiber-reinforced polymer composite materials was measured excavating four laminates, basalt (B14), glass (G14) and their two sandwich type hybrids (B4G6B4, G4B6G4), with 6 mm twist drills at 1520 revolutions per minute and 0.10 mm rev−1 under dry running with an uncoated high-speed steel (HSS-R), grind-coated high-speed steel (HSS-G) or physical vapor deposition-coated (high-speed steel coated with Titanium Nitride (TiN) and Titanium Aluminum Nitride (TiAlN)) drill bits. The hybrid sheets were deliberately incorporated to clarify how alternating basalt–glass architectures redistribute interlaminar stresses during drilling, while the hard, low-friction TiN and TiAlN ceramic coatings enhance cutting performance by forming a heat-resistant tribological barrier that lowers tool–workpiece adhesion, reduces interface temperature, and thereby suppresses thrust-induced delamination. Replacement of an uncoated, grind-coated, high-speed-steel drill (HSS-G) with the latter coats lowered the mechanical and thermal loads substantially: mean thrust fell from 79–94 N to 24–30 N, and peak workpiece temperatures from 112 °C to 74 °C. Accordingly, entry/exit oversize fell from 2.5–4.7% to under 0.6% and, from the surface, the SEM image displayed clean fiber severance rather than pull-out and matrix smear. By analysis of variance (ANOVA), 92.7% of the variance of thrust and 86.6% of that of temperature could be accounted for by the drill-bit factor, thus confirming that the coatings overwhelm the laminate structure and hybrid stacking simply redistribute, but cannot overcome, the former influence. Regression models and an artificial neural network optimized via meta-heuristic optimization foretold thrust, temperature and delamination with an R2 value of 0.94 or higher, providing an instant-screening device with which to explore industrial application. The work reveals TiAlN- and TiN-coated drills as financially competitive alternatives with which to achieve ±1% dimensional accuracy and minimum subsurface damage during multi-material composite machining.