Legal Question in Immigration Law in California

He can't gain residency without going back to Mexico if he came to USA illegally 3 years ago. He will need to go back to Mexico and apply for a visa and a hardship waiver (assuming that his illegal entry 3 years ago was his first illegal entry to USA).

Under different circumstances, people can apply for a 'green card' without having to leave the country, but it doesn't appear from your post on this forum that he qualifies.

You should consult a lawyer before attempting to file any petitions with the DHS.

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Your husband will not be able to adjust his status in the U.S. since he entered the country illegally. In order to apply for an immigrant visa he needs to leave the country and apply for it at the US Consulate/Embassy in Mexico. However, since he has been present in the US illegally for over a year he is now inadmissible and subject to a ten-year bar. He might qualify for a waiver of inadmissibility if he meet the requirements.