Importing multi mesh model from Blender

Hey guys, I've been battling this for a little while. I have this simple model I made in blender, everything is one mesh except for the eyes. I tried to parent them to the armature as well so they would follow the head during the animations.
I got it to work but when I import the FBX into unity, you can only see part of the eyes depending on the angle you look at them front.
Here's a gif of how it looks
I'm really new to all of this so I'm lost! haha
I've attached the .blend and fbx files below

Thanks!!

 

It looks like either the normals are flipped (faces in 3D can usually only be seen from one direction unless you chose to render both sides) so you need to flip those faces the right way in Blender, I think you select the faces and then it's CTRL-N in edit mode, the hotkey could be different though, I haven't used Blender in a while

If that isn't the problem then it's likely you have z-fighting going on and just need to move the meshes slightly further apart as they're conflicting for space

Cool model by the way!

 

Thank you!! Turned out to be the latter, z-fighting, just moved the eyes forward a touch and that fixed it.

 

Glad you got it sorted!