I'm not really sure about Corda, but as far as I know, there is no possibility to get them to communicate on a blockchain-layer since this would require sth in the direction of MultiSignature transactions.
My actual answer:
It seems you will have to do it the old-fashioned way and build APIs on both sides and then make sure communication is secure and valid.
You could do sth. like syncing them on a database-layer level, but this will be ugly as f*** and I would highly recommend against it, since you could easly compromise security AND integrity of you whole system.
Sorry I'm mostly providing #FUD, but the corporate blockchains are far behind the development of the Open Cryptocurrency- and Smart Contract Community.