What's the procedure in marrying a person with a F1 status?

Individuals who enter the country legally like your husband and marry US citizens are allowed to adjust status to permanent residence even if they are no longer maintaining their legal nonimmigrant status. In an interview, the focus will be upon whether you have a bona fide marriage rather than on whether he has maintained his F-1 status.Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.  

Hello. You can file for his adjustment of status, but must be careful with the applications. Marriage to a US citizen cures any violation of overstaying this type of visa.  Assuming he does not get notification from his school or USCIS for his SEVIS violation, you should be fine. But, I recommend filing soon before the school informs the USCIS.  Let me know ifyou would like any assistance.