need to apply for permanent residency, but am currently working illegally.

First of all, congratulations on your marriage!

I strongly suggest that you speak with an immigration lawyer concerning your husband's situation. You mention that he has been here illegally for 14 years, but what I would need to know is how he first entered, and whether anything has ever been done during the time he has been here to try to get permanent residence.

You see, being married to a citizen only helps if he entered legally and then just overstayed as opposed to having snuck in across the border without a visa (entered "with inspection" as opposed to "entered without inspection"). Having been here illegally, even if he worked without authorization, is forgiven for people applying based on marriage to a citizen as long as they entered legally and can prove it with the I-94 card stapled into their passport upon entry (there are ways to replace this if it was lost, but not if none was ever issued). Entering legally would be the only way your husband would be eligible for Adjustment of status to a green card in the U.S., without leaving.

Otherwise, he would have to leave to process abroad for a green card - and leaving after being here illegally subjects him to a bar to coming back (ten years, for being here more than one year illegally and then leaving). There are waivers of this bar available based on a high level of hardship to a citizen spouse or parent, but these aren't easy to get.

There used to be a way someone who entered illegally could still apply for a green card here by paying a $1000 fine, and some people are still eligible for this if they had some form of green card case on file before April 30, 2001 -AND if that case was approvable at the time it was filed. So, having been here 14 years, it is possible that your husband tried to get a green card long ago and just never finished that process - thus becoming eligible to apply here based on your marriage combined with that old case.

This all gets complicated, and there are other things to consider (whether he got the social security card legitimately or whether there might be some document fraud issue, whether some other problem might come up).

So, it is really important that you and he speak with a qualified attorney. Good luck!