This could be a problem. Your husband and you should have thought about this before he overstayed his 90 day visa by over one year. HIre an experienced immigration attorney to handle this matter.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
Usually you cannot file an adjustment of status from VWP status. As a general rule, a person who enters on VWP cannot adjust status to lawful permanent resident status (green card holder) while in the U.S. By entering on VWP, you certify to the Customs and Border Protection agent who admits you that you do not intend to stay in the U.S. If you intend to stay in the U.S., you are considered ineligible for the VWP and should seek the appropriate visa from the U.S. consulate in your country.
The exception to this is for immediate relatives of U.S. citizens who are the beneficiaries of an immediate-relative petition and file an adjustment of status application within the 90 day authorized period. Sometimes, after people arrive in the U.S. on VWP, they might change their minds and decide they want to stay permanently with their U.S. citizen family member. If you are in the U.S. based only on the VWP, then you can file for a green card based on marriage to a U.S. citizen, or being the child of a U.S. citizen (under 21 years old and unmarried), or being the parent of a U.S. citizen, and the U.S. citizen child who petitions for you must be 21 years or older (these three bases together is called the “immediate relatives” category). However, a VWP holder who files for an AOS outside of the 90-day period or is otherwise placed in removal proceedings may be ineligible for an adjustment of status, even if they are an immediate relative. For all other kinds of green card applications, you will still have to go through the consulate in your country after the initial petition has been approved by the USCIS.