The present work reveals the machinability characteristics of Al7068/Si3N4/BN hybrid composite materials. The composite materials were prepared through the liquid metallurgy technique with various weight fractions (0, 5, 10) of silicon nitride and hexagonal boron nitride particles. The experimental studies were performed on a CNC milling machine by varying cutting speed (600, 1200 and 1800 rpm), feed rate (150, 300 and 450 mm/min), and depth of cut (0.8, 1.2 and 1.6 mm). Taguchi’s plan of experiments (L27 orthogonal array design) and analysis of variance (ANOVA) were employed to investigate the effect of process parameters on surface roughness (Ra), cutting temperature, and material removal rate (MRR). Taguchi‐based grey relational analysis (GRA) was performed to identify the best process parameters combination for optimising the multiple responses simultaneously. ANOVA results revealed that the weight fraction of Si3N4 is the most contributing parameter for multiple response characteristics.