Normally, yes, after you acquire Italian citizenship, your spouse is eligible, but you must first register your marriage in Italy, prior to applying. Spouses of Italian citizens can apply for citizenship after two years of marriage if a couple is living in Italy and after three (3) years of marriage if they are living abroad. When applying, if these time periods have already been met the process is immediately started. Also if you have a child, the time is cut to 18 months in both Italy and in another Country. Foreign women who married Italian men prior to 27 April 1983 automatically acquired Italian citizenship, and thus are entitled to apply simultaneously with their husband. This is a request and not a right. To learn more about the requirements and the process, FOLLOW THIS LINK