If someone was unlawfully present in the U.S. (or was deported) and then left the U.S. and returned unlawfully after 1997, they are permanently barred from becoming a permanent resident of the U.S. However, if they remain abroad for 10 years, they can apply for a waiver (using form I-601) of the bar if they can demonstrate that their spouses and/or parents who are either U.S. citizens or permanent residents would suffer "extreme hardship" if they were not allowed to return to the U.S.
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The I-601 form is used to apply to have certain grounds of inadmissibility (issues that make someone ineligible for permanent residence without a waiver) waived. A waiver is not available for illegal Re-Entry after,for example, removal from the U.S./previous unlawful presence of a year or more. I would still suggest you speak to a competent immigration attorney to pin down the facts of your husband's case and assess relief.
There is another challenge to your husband's decision to return to the U.S. and find a lawful solution. He may be charged with unlawful re-entry, which is considered a Federal Criminal Offense. If he is found or pleads guilty, he can be sentenced to imprisonment in a Federal Jail. His decision to return after what 'may' be an official removal order creates an indefinite bar on immigration. An experienced attorney should look at his FBI and/or Immigration file. This can take time to secure.
The ten year period outside the U.S. is required before he 'can apply' and have his form I-601 reviewed by a U.S. Official. He can be required to prove his ten years of presence in Mexico. If the U.S. Government accepts the form on that tenth anniversary in Mexico, then it can review and decide whether he qualifies for a waiver of inadmissibility.
Usually, even after ten years of separation, the U.S. Citizen/permanent resident spouse or parent must still prove that the Citizen or lawful resident will suffer extreme hardship due to this physical separation or life abroad. This should be done to the satisfaction of the U.S. Citizenship and Immigration Service based upon past official decisions. How and whether an applicant can prove that they will suffer extreme hardship is best reviewed by an experienced immigration attorney.
The above is general information and does not create an attorney client relationship.