Since you are married, have you filed the I-130 relative petition? After that is approved, he will file for an immigrant visa at his home consulate, but will need a waiver for the immigration violations. Each consulate has different procedures, but usually, you apply for the IV, the CONOFF determines he is not eligible because of the immigration violations, requests the waiver, you present the packet and it is reviewed by the CONOFF, then the IV Chief, then sent to the Admissibility Review Office (ARO) in Washington DC for a final determination.
To qualify for a waiver, he will need to prove up the extreme and unusual hardship to a qualifying USC relative, in this case, you as his spouse. The most common hardship waivers are approved because of severe medical conditions you have. Other factors are financial, if you have children enrolled in school, other USC relatives you care for, the country conditions in his home country, your ability to adapt and work in his home country, etc.
You should consult with an experienced immigration attorney and he/she will likely refer you to an experienced psychiatrist/psychologist that can prepare a professional assessment regarding the emotional/mental hardship
With his fingerprints, the USCIS and CBP will be able to see if he has any other immigration violations. Don't lie about anything.
These cases are very fact-specific, so not easy, even for experienced practitioners, check with AILA or your state bar for a reference. Good luck.
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