Machining of multidirectional Hybrid Fiber Reinforced Composite (HFRC) is a challenging task because of defects like matrix cracking, fiber pullouts, delamination, burr formation, and heat affected zones. The current study is focused on machining and characterization of in-house fabricated HFRC made of carbon and silica glass fiber using Abrasive Jet Machining (AJM). Machining of holes in fabricated multidirectional HFRC has been carried out using a set of input machining parameters -air pressure, abrasive grit size, and standoff distance. The output responses selected for the experiment are material removal rate, circularity, Depth Averaged Radial Overcut (DAROC), Taper Angle (TA), and Surface Roughness (Ra.) A novel technique has been contrived for measuring DAROC by using Computerized Tomography images. At the same time, the microstructure, surface roughness, and burr height of the machined samples are carried out using High-resolution Scanning Electron Microscope (HRSEM) images and 3D-profilometer images. Subsequently, the machining parameters are optimized using multi-objective GRA to strike a balance between the output parameters. The obtained results indicated the absence of defects like delamination, burr formation, heat affected zones in the machined samples. The outcome of the experiment corroborates the application suitability of the AJM process for machining multidirectional HFRC used in industrial and commercial products. © 2020, Springer Nature B.V.