When applying to get your permanent residency, you usually have to provide proof of the relationship for your dependents. Generally this is in the form of a marriage certificate. If that is not available, you may have to compile additional evidence of your relationship to qualify your partner as a derivative beneficiary.
Under current U.S. immigration policy , same sex partners in a valid relationship may apply for permanent residency to the U.S. under the EB-5 program. However, the same sex partnership has to be recognized in a legal marriage relationship in their home country first before they file for residency to the U.S.