community and separate debt under WA state community law

WA is a community property state. If the credit card bills were incurred before marriage and/or you are not named on the account they are his separate debts. You have no obligation to support his children unless you have adopted them.

RCW 26.16.205 (Liability for family support – Support obligation of stepparent) provides: "The expenses of the family and the education of the children, including stepchildren, are chargeable upon the property of both spouses or both domestic partners, or either of them, and they may be sued jointly or separately. When a petition for dissolution of marriage or state registered domestic partnership or a petition for legal separation is filed, the court may, upon motion of the stepparent, terminate the obligation to support the stepchildren. The obligation to support stepchildren shall cease upon the entry of a decree of dissolution, decree of legal separation, or death."

Whether a spouse is liable for the debts of the other spouse depends on the specific facts including what is the nature of the debts, any agreement between the spouses.

If you arrived in the US on a family-based immigrant visa sponsored by your husband, there are immigration issues.

You likely should discuss the facts and options of your case with an attorney.