You may be eligible for immigration benefits. Yes, the I-360 can lead to a green card. However, no one simply completes an immigration form. The evidence that accompanies the form is extremely important. There are other ways to obtain evidence that your husband is a citizen of the US. Seek assistance from an immigration attorney. Good Luck
I recommend contacting a qualified immigration attorney to fully evaluate your case to see if you can self-petition as an abused spouse. It is difficult to address these types of cases in this kind of online forum.
Legal disclaimer: By answering this question, there is no intention to create, nor does it create an ongoing duty to respond to questions. An attorney-client relationship has not been formed. The answer is not intended as anything other than the opinion of the author. It should not be relied upon as legal advice. The answer given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change.
The short answer is ... yes. Now, here are some particulars ...
First the I-360 must be approved by USCIS. Once you receive and approved I-360 you will be eligible for a work permit or to apply for adjustment of status; depending on your particular situation. You might be eligible to apply under VAWA and file a concurrent I-485. A lot of factors can determine your eligibility and the right process for you. It is extremely important that you present a solid, well documented, case.