I don't think you can do this with an external answering machine and an internal fax. This is because one of them has to answer the call before detecting the type of call, voice or fax.
I have a fax machine that will answer the call, if it is a voice call it's supposed to ring the telephone. Never used it so I don't know if it works!
An internal answering machine such as click here should do the trick, though it's not clear whether the fax needs to be external or not.