If community-property rules apply, as they do in 99% of marriages in the DR, the surviving spouse is considered the owner of 50% of matrimonial assets. This 50% is not a part of the inheritance and therefore no inheritance taxes are due.
Spouses are not regular heirs under Dominican law. If a spouse dies, the inheritance goes to the children. If there are no children, it goes to the siblings and the parents. If there are no siblings or parents alive, it goes to other relatives. Only in case there are no relatives up to the 12th degree will the husband or wife inherit.
This is the situation if the spouse died without a will. It is possible to leave assets to the surviving spouse by writing a will, although there are restrictions on what can be given: only 25% of the inheritance if the deceased has 3 or more children, no more than 33% if case of 2 children, no more than 50% in case of an only child.
If you accept the inheritance you will also be responsible for the debts. You may accept conditionally (?bajo beneficio de inventario?) until the assets and debts are sorted out with the option to decline the inheritance in case there are more debts than assets.