I accidentally transferred the money from coinbase BTC account To Bittrex BCH account. It has yet to show up in either accounts. Can someone help?
I realise the question is a few months old, and no response from OP, so maybe resolved.
But to answer the question for anyone stumbling across this in future, there's a good chance the coins can be recovered for now, but it depends on the address used. If it's a "1" address, then the private key can be used by both bitcoin cash and bitcoin. It's likely a manual task for the support team though, so unlikely they will be too happy about this!
Sending to a "3" address may be different, if it's a plain old multisig it could be recovered (I believe, as that's not been tampered with), but if it's a SegWit address, it may be recoverable - for anyone! Bitcoin cash has no concept of SegWit, so the coins really are "anyone can spend", and in fact someone did claim them all at one point (not sure on the ethics/legality of that one, but that's another topic).
Immediately after the release of the bitcoin cash fork, all bitcoin addresses were valid on the new chain. The good news is bitcoin cash is switching to a new address type see this question, so should cut down on the amount of issues this will cause in future.