Drilling Phenolic

Clamp it between 2 pcs of wood and drill thru the sandwich. This works a charm for plastics, fiberglass, leather, thin metal sheets, etc. Art

Small-ish pilot, then an endmill? Whatever method, do from both sides? Or sandwich each pc between wood, or sandwich a stack, well-clamped.
High-ish rpm might help, 3K+.

You've got thin material that will ride up the drill unless clamped securely and backed up with sacrificial material. Might be okay with maximum spindle RPM (8000+ isn't too fast with carbide), particularly if you drill a smallish pilot hole first.
Best regards, Spehro Pefhany

It's been a few decades, but it actually machines quite well. As the inexpensive, non-magnetic, reasonably strong insulating material of choice I used a LOT of in in various plasma-physics related work. Sharp tools - and carbide is a good idea, as it makes most softer tools dull quickly (but they will be fine if you're only doing a few holes and they are sharp to begin with.)
1/8" is a bit on the thin side.
If you do have problems with drills, try end-cutting endmills, solid carbide, - if you don't have a mill, in a plunge router clamped to the work (get 1/4" shank endmills so you can find a router collet to fit.)