If you earn enough disability that you, your children, and he will be at 125% of the poverty rate, then you can. Otherwise you need a joint sponsor.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
We would need more information in order to know for sure whether he would be eligible to adjust status in the United States. You mentioned that he has an I-94 in his passport. Is that from his most recent entry to the USA?
Again, there are many more questions that would need to be asked in order to determine if he could adjust status in the USA. I suggest that you consult with an experienced immigration attorney, to have the best chance of success.
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You certainly can petition him and he can adjust here in the US. You should seriously consider hiring an immigration lawyer to prepare the various forms and guide you through the entire application process.
Generally, a US citizen can file an immigrant petition on behalf of his/her foreign national spouse, based on which your foreign national spouse can adjust his status if he entered the US lawfully (i.e. with valid entry document) and does not have any criminal issues. As a part of the adjustment of status process you as the petitioner will be required to show that you have sufficient income to support him. Since you have three kids, your household size will be 5 after you count everyone, therefore, you should have at least the yearly income of $33,762 to meet that requirement. If you don't meet this income requirement you can use a co-sponsor for the completing the affidavit of support. I would highly recommend hiring an immigration lawyer.
Attorney at Law
Parikh and Prasad Law Group
You can file for him, when you are married. As the other attorneys stated you may require a joint sponsor. I would highly recommend you work with an attorney. Many, including myself offer payment plans. We also have offices nearby in Westchester and NYC.
Law Offices of Nicklaus Misiti
212 537 4407
Legal disclaimer: The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.