Can my husband ever re-enter the U.S.?

Even though your husband was not deported, he is likely inadmissible (ineligible to enter the U.S.) for 10 years because of his overstay. Depending on the exact formulation of his convictions, he might also be permanently inadmissible as an alien convicted of an aggravated felony. Certain relatively minor offenses, misdemeanors and even some violations, are considered by immigration law to be aggravated felonies that permanently disqualify the convicted person from admission to the U.S. and all benefits under the immigration law. Although you did not specify what sexual misconduct your husband admitted; so many sexual offenses are considered aggravated felonies that it is should be assumed that your husband is permanently inadmissible for an aggravated felony conviction. You should ask an immigration attorney to review your husband's criminal record to ascertain whether this assumption is correct . Your relatives are correct: the only way he might obtain permission to re-enter the U.S. any time soon is if you obtain a waiver of inadmissibility for him. You chances of obtaining this waiver depend on a) how serious were your husband's convictions and b) how badly his absence affects your life (the waiver is granted to U.S. citizens who suffer "an extreme hardship" as a result of their alien spouses' inability to enter the U.S.; "mere separation" and loss of the second income is not considered enough). A competent immigration attorney should review your family circumstances and tell you what are your chances of getting a waiver application approved.

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. (S)he 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.

There are "waivers" available to spouses of U.S citizens . You need to consult an immigration attorney and apply for a waiver after the visa petition is approved and at the time of the interview. It appears from the nature of your question that there are already some marital problems. So think about all issues before you apply.