Student and advisor applying to same job - conflict of interest with recommendation letter
It is helpful that you and your advisor have been in contact and have honest communication about this subject. It's commendable, and doesn't happen nearly often enough.

That said,, for this particular job, if you want to have any realistic chance of getting this particular job, you really need to have someone else replace this particular co-advisor. Otherwise, a rather confused hiring panel may take a look at both applications, wonder what the heck is going on, and throw out both applications.

However, for any job in which you're not in direct conflict, I think it would probably be OK to have your co-advisor as a letter of reference.