I may be wrong here, but in a divorce, I don't believe there is any gift tax issue to be concerned about. I'm pretty sure that H can just give you half that account as part of the marital settlement. If he is trying to tell you there is a gift tax issue then he is probably lying.
Have your own consultation with an accountant. Also, in making terms for a settlement, make sure to consider the tax ramifications of everything. Examples:
-Alimony is deductible to the person who pays it and taxable to the person who receives it.
-If you keep the marital home and your equity in it exceeds the allowance for tax-free profit (still 250k for an individual, I believe, and 500k for a couple?) you will pay capital gains tax on the excess when you sell. If you might sell in a year or two, may be better to sell now (before divorce, when you can use the whole 500 k exception).