DON'T DO IT

Beacuse the new bank where you refinancing from needs to reassign the lien hoder on the deed.  That requires the existing owners on the deed to sign the document in order the make such change as well as removing any one from the dead.  There is no way to refinance the house first and remove one of the owner later.  It needs to be done at the same time by the title company.  Even there is a way allows you to do so, but DO NOT do it.  If your EX does not sign it, that means he DOES NOT intent to exit from the ownership of the house.  He just attempt to lie to your and have you take over all the liability of the loan but keep him as the owner of the house.  so STOP and consulte with attorney to find a clean way for your seperation.  Good luck.