Who is responsible for the final costs of my almost ex-husband?

Married people are not responsible for the individual debts of their spouses unless they have taken on the debts themselves, like when you co-sign a loan. So, even though you were still married at the time of his death, you aren't responsible for your husband's funeral expenses.

If you make funeral arrangements for your husband, make sure that it is clear that you are acting as the representative of his estate and not individually. Don't put any of these expenses in your own name. Funeral debts are a debt of your husband's estate and should be paid before anything is distributed to his heirs. Whether your husband died with or without a Will, as his surviving spouse you will be in a position to inherit from your spouse after his final expenses -- including funeral costs -- and debts are paid.