Your husband can only adjust his status based on marriage to a U.S. Citizen in the U.S. if he entered lawfully or if he had an immigrant petition filed in his name prior to April 30th 2001. An immigrant petition is a petition for a greencard, a visitors or work visa applicatin does not count.
If your husband entered illegally and did not have an immigrant petition filed for him prior to April 30th 2001, then he will have to consular process in his home country. Once he leaves the U.S. he will be barred from returning for 10 years. In order to get a waiver of the 10yr bar you would have to show that you would suffer extreme hardship if the bar were not waived.
These kinds of cases are difficult and can be complicated. You will need to work with an attorney and discuss your situation in detail. The above information is general in nature and not specific legal advice. More information is needed as there are more variables such as criminal history and other factors.
Andre Olivie, Esq.
If your husband entered with a visa in his name he did not enter illegally. If however he is married to a U.S. citizen he could file a petition and then would also need to file a hardship waiver which would be difficult depending on the facts. In the alternative he could file the petition and then leave but then he would be subject to another waiver for the 10 year bar due to his unlawful presence so this would be even more difficult. Either ways he should get an attorney as these cases are difficult.