Your parents should have registered their marriage with the local authorities at the location where they married. They need to apply for a certified copy of their marriage certificate.
Otherwise, contact the local U.S. Consulate regarding a DNA test for your visa petition.
showing each parent's relationship to you is key, not to each other. you can petition for them even if they were not married to each other but both are still your parents. even with DNA you will have to show that your father acknowledged you as his son and supported you until age 18. you should really hire an immigration attorney for this case.
Please be advised this answer is for informational purposes only and no attorney-client relationship has been formed. You should also see a local attorney for legal advise before acting on any of the statements given to you online as there may be aspects of your case that are not obvious by the question asked online.