in divorce, husband wants equity cashout, what happens if bank finds me inelligible for higher debt

Presumably you are talking about the equity in your home. If you plan to keep it as part of the divorce, you first need to determine the value and equity; you can agree upon the value, use your property tax bill or have the home appraised. The equity is determined by the fair market value less the current mortgage loan payoff; once the equity is determined, you will need to go to the bank or a mortgage lender to refinance and have the loan pit just in your name and pay your spouse half the equity. If you cannot accomplish that, presumably the home would have to be sold and each of you split the equity at sale. You can also consider using other marital assets to pay him half the equity. If they have a pension or 401k, you could consider your 50% share of those assets against their share of the equity they are entitled from the house. You would still need to refinance the mortgage into only your name, butvtgis might avoid having to borrow more money to do the cash out.