Unfortunately, because he is not a US Citizen, there are no visas immediately available for you to be able to legally stay in the US to complete the process to the green card. If you do stay, you will be out of status, and will probably be able to adjust your status once he becomes a US citizen.
If your husband files for a green card for you now, it could take about 4 years for a visa to become available for you. I agree that it might be better to wait for him to become a U.S. Citizen and then adjust your status.
Seeta L. Nangia, Esq.
Law Offices of Seeta Nangia
Exclusively Practicing Immigration Law
Phone: (415) 273-9123