So Diffie-Hellman is subject to a MITM attack where two parties exchange:
X = g^x mod n and Y = g^y mod n.
Now presumably this can be protected against by using the Rivest Shamir interlock protocol where we split a message into two pieces and exchange them bit by bit. What I want to know is how we can split g^x mod n into two pieces for usage with Rivest Shamir?
Have you actually read the paper by Rivest and Shamir? It explains quite well what the protocol is for and the scenario that it's designed for:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.159.1673&rep=rep1&type=pdf
I don't see how this is very applicable to Diffie-Hellman, since the point of the protocol is to authenticate public keys not to actually generate private keys.
If you're just interested in implementing Diffie-Hellman, then you need to choose a concrete group for your DH implementation and a bit encoding for its elements. In practice, you do not actually use the direct bit encoding of your group element as a key, but you apply a randomness extractor that gives you a bit string that you'll use as your key.
Randomness extractors are quite tricky, but there are some recent papers on them which you can easily find with google.
