Thanks for your inquiry. Sounds to me like the answer to your question is that you would appear qualified to apply. This is one of those circumstances where the law makes little sense, but it is what we have. Let me explain.
The way that the law is written, most individuals applying for resident status here in the US must establish that the individual is validly maintaining non immigrant status (or some other qualifying status) at the time that the application for adjustment of status is made on the Form I-485. However there are certain exceptions to this rule. One of those relates to "immediate relatives" which are defined as unmarried children (under 21), parents and spouses of US citizens (USC's).
If you are an immediate relative then the only requirement for you to establish is that you lawfully entered the US (or were paroled into the US). You would appear to be an immediate relative as the spouse of a USC and it appears that you entered the US lawfully, so you seem good to go if you can otherwise establish eligibility for adjustment of status (i.e. no issues with any ground of inadmissibility and you can satisfy the Affidavit of Support requirement).
Where the law makes little sense is that if you did not enter the country legally (i.e. entered without inspection) then you are not qualified. At various points in the past, we have had the availability of §245(i) of the law which is a provision which would permit individuals who have entered the US without inspection to apply for adjustment of status. This law IS NOT currently in effect and was last active for petitions filed on or before April 30, 2001. In your case, however, §245(i) is not needed for you to qualify.
While I see little difference between folks who have come to the US and have remained in violation of their status as opposed to folks who came to the US initially by violating the immigration law and entering without inspection, the Immigration and Nationality Act draws a distinction between these two classes of individuals and the law is as the law is.
So what I would suggest to you and to your spouse is to consult with a qualified attorney and get the lay of the land. I tell clients that I do not think that the application process associated with what it is that you need to do is all that complicated, I do believe that hiring an attorney can make it go correctly the first time. It is confusing, the instructions make absolutely no sense and the assistance of an attorney is probably a really good idea.
Looks to me like this is a relatively straight forward application, just make sure that you have a good grasp of what is required, the forms that must be filed and the fees which are associated with the applications process. Good luck.
Attorney Stoller's response was very clear and detailed and I agree with him. I believe you need to find an experienced immigration attorney to review your entire immigration history and to work with you on the case. Best of luck to you!
Sounds like a good case but I'd encourage you to retain counsel to ensure compliance with all relevant laws including eligibility to adjust status (INA 245(c)) and admissibility (INA 212(a)). These are routine cases for experienced immigration lawyers.