If my husband was deported to Mexico a year ago for just being illegal, is there any way I can fix his papers?

You can only bring him back to the US once he has satisfied the conditions of his deportation order unless he can prove extreme hardship.

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your situation. He/she would then be in a better position to analyze your case, advise you of your options and, if possible, make sure that the necessary paperwork and documentation is presented so as not to delay the process.

It may be possible depending on his previous immigration history in the United States. At a minimum, you will need to submit an I-130 relative petition on his behalf.