If you entered the U.S. with a visa and overstayed, you may adjust status to a permanent resident alien (green card).
There is a good chance you may not be able to adjust if your wife is only a green card holder and not a US citizen because in that case you do not qualify as an immediate relative and your unlawful presence will prevent you from adjusting your status. If you overstayed for less than 6 months, you can still return to your country and try consular processing. If you overstayed for longer than 6 months or 1 year, and if you return to your country you will incur a 3-year or a 10-year bar, respectively, and you may need to apply for a waiver of inadmissibility.
I agree with Ms. Bucin. Your options are limited until your wife can file and become a naturalized U.S. Citizen. How many years has she been a lawful permanent resident? Can she read, speak and write enough English to take the examination? Is there any reason why she cannot file for naturalization due to some sort of disqualification? Has she left the U.S. for an extended period of time?
These, among other issues, should be reviewed by an experienced immigration attorney. Should you desire legal advice, our office is also located in Chicago. Good Luck.
The above is general information and does not create an attorney client relationship.