This has happened to me several times. Am I missing something? Here’s what’s happening

1)Find faction outfit

2)give to your companions to hold

3)screen says, companion can’t wear this.

4)Item disappears from both my character's and my companion’s inventory

I haven't had or heard of this problem.

I guess just don't have your companion carry it.

When I put a legion armor on Boone he just threw it out and it was next to his feet.

maybe this is happening, thanks for the feed back. I'll watch for this next time i find some faction apparel

For some reason it never dawned on the developers you might actually want your companions to CARRY the armor rather than wear it. So... They attempt to wear and rather than return it to their inventory, they'll drop it. They could have added an option to specify the armor to wear, ask the companion to put on the best armor, or even just have them realize they can't wear it and not bother removing it from their inventory... And the developers did none of that. It's a gross case of stupid overall. It'd sad when Fallout 2 offered better companion control.