There is a separate form for jure matrimoni applicants which you can obtain from the NY consulate's website under Services, Consular Services, Citizenship, Citizenship by Marriage to an Italian Citizen. I would post a link but these have not worked in the past. The site also contains pretty good instructions of what you need to do.
For your application your husband does not have to do anything. Once you are recognized and your marriage is recorded in your comune then your husband can apply. This of course assumes that you have been married long enough and otherwise qualify.
If you don't live in the jurisdiction of the New York consulate, I would recommend that you obtain information from the website of your own consulate or that of the Italian Embassy site in Washington, DC., which has more accurate info both in Italian and English.
Yes, to clarify JJ's post above: Your husband cannot apply during your appointment. That is a second step, and it is not automatic. First you must obtain your own dual citizenship. You will have to see if he is eligible based on your marriage date especially (if it was later than 1983, I believe, the process may be more complicated). Then, if he is, you will have to register your marriage in your commune in Italy (after you are a recognized citizen), and thereafter your husband would be able to apply via marriage.
Date of marriage is not a factor with a male spouse. A woman automatically became an Italian citizen if she married an Italian man before 1983. This automatic citizenship never applied to the husband of an Italian woman. Since your marriage certificate is submitted with your application packet, your marriage will be registered as a final step in the citizenship recognition process.
If you have been married for at least two years, your husband can apply for citizenship after your citizenship is recognized. This is a naturalization process that will take from two to three years.
There are different steps that you have to take with this, for starters, it would not always be good to get dual citizenship because it would be hard for you to take part of something that you are not. But in all fairness, marriage is the easiest link for you to be able to do so.
And you just have to see how things are going to work properly in those terms and see how they are going to be made available.