Did your husband enter the country legally with a passport and then overstayed? Or did he enter the country illegally?
If the former, then you can file the I-130 on his behalf and he can file to become a permanent resident. If the latter, then while you can file the I-130 on his behalf, he is unable to adjust status at this time unless someone else filed an immigrant petition on his or his qualifying relative's behalf prior to April 30, 2001 thus grandfathering him in under 245(i).
At this time, by filing the I-130, you risk putting him into deportation proceedings because he is illegal, however there could be a possibility of cancellation of removal if he has never been arrested, paid taxes and can show extreme hardship to qualifying USC relatives if he was deported.
You will want to consult with an experienced immigration attorney before you file anything to run through the possible scenarios and accompanying risk factors.
I will agree with the previous attorney on the steps. Make sure that you check with an immigration attorney before you proceed. You do not want to file something that will result in him getting deported. Also make sure that his criminal background is cleared before filing any sort of immigration paperwork. Check the article attached regarding marriage and the greencard.
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I recommend that you meet with an immigration lawyer in person or over the phone to provide more details and get the case evaluated.
It is possible for your husband to adjust his status in the United States if he entered with a valid visa. Did he enter with a valid visa? Are you a U.S. citizen? You could file a Marriage Green Card Petition for him if this is the case (I-130, I-485). In addition, your husband might qualify for 245i relief.
You should not file any paperwork with the U.S. Immigration Service alone under these circumstances. Please obtain an immigrationlawyer to help you.