DC recognizes common law marriage. Therefore, if you are male and female and have held yourself out to the community as husband and wife, you are in a common law marriage. If you are the same sex then you would need to meet the criteria for domestic partners.
The determination of your question may have an impact on your status with regard to each other's benefits. Accordingly, you may wish to consult with an attorney.
Please be advised that any information or advice given herein does not constitute an attorney client relationship. Further, before taking any actions or deciding not to take any actions, you should seek counsel of an attorney. This forum cannot provide you with the anyalysis and detail necessary for a full and accurate opinion to be rendered.
To some extent, the answer depends on what you want to achieve. In general, in DC, if you call each other husband and wife in public, that's enough to establish a common law marriage. I see that you have a tag on this question of "Domestic Violence" so I suspect there is more to this question. My suggestion is that you speak with a lawyer and have a private consultation.