With a drug trafficking conviction on his record, your husband cannot become a US citizen.
All drug trafficking offenses are considered aggravated felonies, which are the worst possible type of offense for immigration purposes. A person with an aggravated felony can be deported, and is permanently barred from reentering the USA. Even attempting to enter the US after an aggravated felony conviction is a Federal felony that can lead to prison time.
In fact, I am very surprised that his green card was renewed and that he has not been deported already.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like this, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.
Foreign nationals can be denied naturalization based on criminal charges. Offenses related to controlled substances are among the most difficult to defend in terms of both naturalization and a possible deportation.
That said, there are defenses and waivers that may be available to your husband. There are books written on the subject -- certainly too much to discuss here. I strongly suggest you consult with a knowledgeable immigration attorney if citizenship is a serious goal.
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