Baffling Model Behavior

Perhaps this is a Blender question, and if so, I'll happily delete it. But since occurring in Unity, I figured I'd ask it here.

I have an article of clothing (just think of it as a 3d model, since I haven't set it as "cloth." I rigged it in Blender, didn't look quite right, so I deleted the "clothes" from the player model in Unity and replaced it as a standalone item. (I know this doesn't affect the model outside of Unity, totally cool with that.) So that's where it gets weird. No matter what, the "front" of the clothes faces me in the scene view, making it nearly impossible to rotate to place it on the character. While the character I'm rigging it on stays facing one way (not in game, just in scene view) the clothes will always rotate on them. Has anyone seen this behavior before? Thanks, and God bless.