What can I do to avoid my husbands deportation?

Unfortunately this is rather common. Prior to 1996 a false claim to US citizenship could be waived. After 1996 it is not waivable except for the most limited circumstances of which your husband does not qualify. My suggestion would be to obtain a copy of your husband's alien file from USCIS. In there should be what the goverment is relying on. Even if the government thinks your husband is inadmissible they still need to adjudicate the I-130 that you filed for him. The issue can then be addressed either before USCIS or if they denied your husband's I-485 (assuming he was eligible to file one) before the immigration judge in removal proceedings. Seems a bit funny that the government would allow him to enter the US after making a false claim to US citizenship. The fact that they did this leads me to believe that there is truth to your story and that USCIS is making a mistake. Sometimes pointing out small facts like this can make a difference.