Ah, thanks for the pictures. Doesn't help my argument that it may be horribly worn on the back, but don't worry, somebody that knows will come strolling along.
It could be from a foreign planchet, that was stuck in a bin that came loose and was minted as an half. It could be just a heavy planchet, near the end of a sheet that was not to specs and punched out. I have found dimes that are real thin. I had one of the guys in our club look at it and it was just a light weight planchet. He is an expert on such things. He has a book on such coins.
I measured it with a micrometer and it has the same specs as other halves. I thought it could be from a quarter thick planchet but the half is bigger.