The judgment (if you can't settle ahead of time) will be only against him.
Once there is a judgment, if he doesn't set up a payment plan, then plaintiff's counsel may eventually decide to execute the judgment by either garnishing (his) wages or attaching ("seizing") his bank accounts.
So no, plaintiff's counsel will not be able to send the garnishment paperwork to your employer to garnish your wages on your husband's debt.
But if you have checking or savings accounts in both of your names, then depending on your state, they may be able to attach the accounts. There are exclusions (social security, etc.) on what they can attach, and some states will separate monies that can be attributed to the separate people on the account. But that will be a lot of work on your end if that happens to straighten it out.
Might be worth it to get an account in your name only where your paycheck is deposited. It can be at the same bank as your existing (shared) accounts.
