So today and part of yesterday I was getting the gigantic VGU Dragbody armor packs and since one of the main downloads was taken down I decided to download the 34 other downloads.
This resulted in more than enough choises of decoration my character, more facemasks then I'll ever need and one issue I had a while before which I thought was the issue of a mod. That is my characters Eyebrows.

My eyebrows clip through facemasks
This is kind of annoying.
I suspect it may have to do with a checkmark in Fallout character overhaul. Or maybe something of Dragraces by Dragbody. 
I really don't know. I have made some screenshots to highlight the issue and maybe someone has some clue as to what causes the eyebrow option.
The eyebrows don't have an effect on default New Vegas characters since it is made for the size of their head and I don't think I ever saw it appear on any custom races.

the issue:

Edit currently I know it is indeed caused by something inside Fallout Character Overhaul 3.0
Removing the file that makes the menu appear didn't fix it so far but I'm sure if I find the individual eyebrows of choosing deleting them might work.

Quote :

deleting them might work.

I doubt it - you would get that red exclamation mark.

I don't have those facemasks, but I think the problem here is that those eyebrows are independent meshes and those masks are probably skintight, resulting in the eyebrow-meshes to be located above the facemask-mesh.

From what I can tell, there's only one eyebrow-mesh for each gender: meshes>characters>hair>eyebrowm.nif/eyebrowf.nif
Perhaps you could just replace that mesh with vacuus.nif
Or you could replace one of the eyebrow-textures with one that is just transparent.
Or you could open the eyebrow-mesh in Nifskope and change its Translation so that the mesh is effectively inside the head-mesh.

@shadowshade Something I noticed which could help is the fact that facemasks as you can maybe see in the screenshot is that they hide the hair and beard. 
Maybe there is a way to make it so the eyebrows hide under armour aswell.
But your suggestion might work too.
Haven't tried nifskope before but I'm sure it shouldn't be that hard with a tutorial or two.

And yes deleting some items just makes an exclamation mark
I found out deleting the menu file didn't work aswell. Since the eyebrows were already loaded or there is a default eyebrow.

Something else I found out that I could try now along with your information is downloading an older version of FCO. Since it currently uses a newer version by Drummer with his standalone version of the brows mod in it.  http://www.nexusmods.com/newvegas/mods/57742/?
There is also a specific meshes and textures folder called Drumber for his eys, teeth and brows. So those are the ones I probably need to edit or perhaps delete.

Of course I would still like the eyebrows to be on the npcs so hopefully there is a way to make that happen.
Hell maybe the eyebrows don't even appear on npcs.


Edit: 
Hell yeah it worked.
So by figuring out the meshes used by the eyebrows mod, I used nifskope to then pick one of the six choosable eyebrows and remove one of the layers.
Removing this layer didn't turn it into a red triangle and just made the eyebrow invisible. 5 out of 6 eyebrows still work. 
My idea was that maybe the least ammount of npc's use the sixth eyebrow.
Well thanks for mentioning nifskope.