I became permanent resident in 2010 have been married for 20 years my husband is in undocumented status we file taxes separately. May I petition him ?

Looking at the September visa chart, the F-2A category for spouses and unmarried children of lawful permanent residence is now current, which means that any immigrant visa petition that you file on his behalf would not take long to bring to fruition provided that the category does not backlog. He would not be eligible to adjust status to permanent residence since he is undocumented, but a choice that you could both think about would be your petitioning for him, having him consul process his paperwork, and upon mandatory refusal by the Consulate or Embassy, file a waiver of the bar for being illegal in the country. (I assume that your husband has no other grounds of exclusion). You could also wait until you become a US citizen before applying and, dependent upon whether your husband entered the country legally or not, be able to have him adjust status here without leaving or go through the I– 601 A program under which he would apply for and wait for the results of the illegal presence waiver application in the States before deciding to go overseas for the immigrant visa interview. Also your husband could wait for the results of action in the House of Representatives on comprehensive immigration reform, which should be decided by the end of the year.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.  

Did your husband enter the US legally and then overstay?  If so, he can get a green card through his marriage to you (assuming you are a US citizen) and he wouldn't have to leave the US.  However,  if he entered illegally, you can petition for him, but he will need a waiver of the unlawful presence bar which can only be issued at a consulate overseas.  However, it is possible to apply for the waiver from within the US so you would know whether you were going to be approved before you left.