Because of your husband's repeated attempts at entering illegally he will have a difficult time reentering anytime soon. If your husband falsely claimed to be a US citizen then he has a lifetime bar from the US (absent very LIMITED exceptions). You should consult with an immigration attorney who can request and review his file and then advise you accordingly.
Samuel Ouya Maina, Esq. 415.391.6612 email@example.com Law Offices of S. Ouya Maina, PC 332 Pine Street, Suite 707 San Francisco, CA 94104
What border patrol might not be making clear is that the 5-year bar attached to expedited removal (if this is what it was) has nothing to do with the other bars your husband has likely triggered and which have very serious consequences:
Fraud in using false documents carries a permanent bar which can be waived by showing extreme hardship to a qualifying relative;
Multiple illegal entries triggers the permanent bar that can only be waived if the person spends 10 years abroad;
False claim to us citizenship, however, is a bar that cannot be waived under the current law.
Unfortunately, your huaband's choices have put your family in a rather unfortunate situation. Perhaps future changes in the law will offer some relief, but the truth is that these kind of issues are probably not going to be excused. I'm sorry.
The information offered is general in nature and not meant to be relied upon as legal advice. Please consult an attorney prior to making legal decisions. Visit us at www.tunitskylaw.com. Contact us at 713.335.5505 or email at firstname.lastname@example.org. Veronica Tunitsky offers in-person, as well as telephone and email consultations.