Since your husband is on a J-1 visa, he will be exempt from the Substantial
Presence Test for the first 2 (if
non-student) or 5 (if student) calendar years that he is in the US. This
means that he is considered a non-resident aliens for US tax purposes.
As a J-2 Visa holder, you will also be exempt from filing as you are considered a nonresident alien. Additionally, you will not be able to file jointly with your husband (who is on a J-1 visa) and will not need an ITIN.
He will need to file a Form 1040NR to report your US
source income. TurboTax does not support Form 1040NR. You may want to try https://www.sprintax.com/ which is specifically designed to help
international student nonresident aliens with their US tax returns.
Click this link for more information from the IRS on US Tax Guide for Aliens
