You need to find out what his status was at that time. File a FOIA to get a copy of his immigration file from USCIS and CBP.
Since he is here now unlawfully, probably EWI and unlawfully, you are at least looking at a 5-year bar, possibly more. To see if he can file here in the US, he would need to be eligible for 245(I), so you need to find out if he was deported and if he ever had a preference petition or labor certification filed prior to April 30, 2001.
If not, then he will need to return to MX to file for the immigrant visa. He will be advised he is ineligible for the visa due to his immigration violations and will need to file for the waiver. This will depend on the extreme and unusual hardship to you and you USC child. You should present an assessment from a psychologist or psychiatrist attesting to the severe hardship if you were separated from your husband.
Consult with an experienced immigration attorney for details. Good luck.
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