Does my husband and I have to live together for me to be able to give his immigration papers?

Either as a US citizen or an LPR "green card", you must amongst other things file an I-130 petition to accord your husband status of a spouse of a US citizen or LPR. The bona fides of your marriage is a crucial matter in this determination and if you are not living in the same household with your husband, this may call into question the validity of such marriage. Although, it is not a rigid and inflexible requirement, the burden of proving that you are eligible for the benefit you seek for your husband if yours and if you fail to convince DHS, that application is subject to being denied. I suggest that you consult with an experienced lawyer.

If you are filing for your husband, typically you would have to live together, unless you can show a good enough reason for you two to live apart and you are able to show a bona fide marriage eve though you are living apart.

Under immigration law, you have to show that your marriage is a "bona fide" marriage which is not solely for immigration purposes. One of the things that immigration looks for when they look at a marriage-based petition is whether the couple is living together. Sometimes, couples have to live apart because they may have jobs in different cities, or one of them is in school and other has to work in a different city to support them, etc., and under such circumstances, if the couple can show that their marriage is still legitimate and they intend to make a life together, than living apart would be fine. But, the bottom line is that you have to show the the USCIS that your marriage is bona fide and that you intend to make a life together with your husband.

There can be legitimate reasons a couple may live apart - such as schooling or employment - but the general expectation is that you would live together. Be prepared to explain your reasons and be able to document them.