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.