The answer to your question will depend on whether you are subject to the two-year foreign residency requirement, 212(e). If so, you need to get a waiver before you can adjust. If not, then you may be ready to submit an application to adjust your status to permanent residence. Since DOMA was overturned, you will not have problems regarding your relationship.
Answered on Nov 17th, 2014 at 4:38 PM