Legal Question in Family Law in Oregon

No, you wll not be liable for your husband's child support debt owing for a child of a prior relationship.

See ORS 108.020:

Neither husband nor wife is liable for the debts or liabilities of the other incurred before marriage; and they are not liable for the separate debts of each other.

Also, ORS 108.050. That statute says:

The property and pecuniary rights of every married woman at the time of her marriage or afterwards acquired including real or personal property acquired by her own labor during coverture, shall not be subject to the debts or contracts of her husband.