I have already moved during pending of my Green card application. You should do some steps for that to be save.
1. Like Phwl advised download the AR 11 from and fill it out and send it to the proper address.
2 AR 11 must have to be done but also important things is call to National Customer Service Center tel 1800-375-5283 and choose option 1 for change of address. The personal assistant will come and get the new address with some questions like No of your file , name etc. You can change address in all of your INS file like I 130, I 131, I 765 etc. Then after a month you will receive a confirmation letter from them explaining all the file have been changed of your address. After that you can breath and all of the correspording letter from BCIS will come to your new address.
3 For your husband and affidivit support there is a form for US citizenship to submit to proper address. You can get in the Bcis web also. When you call they will also remind you which form to send again for change of address rather than calling to them. The granter change of address form, he or you got to call NCSC to tell them that you already moved and your husband also change of address in the BCIS files for affidivit support. If you call for him he must be along with you and they will confirm by telling few words to him. You cannot call for him a lone. Then you will received confirmation letter for him also after a month.
4. Please call within 10 days after moving. Please don't call before moving.
5. If you just submit the AR 11 form only the BCIS computer system still have your old address and sometimes Ar 11 donot update the address in your BCIS file easily and might have delay for other correspondence.
My I 131 advance perole and new EAD received without any delay after moving.
Hope this help.