Your co-sponsor needs to fill out an I-864, but if your husband has been working lawfully in the US, he may be eligible for an exemption from having a sponsor. You should meet with an immigration attorney before filing any paperwork for your husband not only to make sure he is eligible for an adjustment of status, but that your petition and his application are properly completed and more likely to be approved.
You cannot sponsor your spouse for citizenship. Only the spouse can sponsor himself. If the quesiton is about affidavit of support for an intended immigrant, yes, any permanent resident or US citizen with qualified income can file I-864.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.