If my husband is the only one who works and therefore has the only income tax, can his income tax be garnished for default of my student loan?

Not unless he signed for the loans.

Not unless he signed for the loans.

What if we file jointly? Is the income tax money considered my money and they will be able to take it?

Well yes, if you file jointly then the return is a joint return and the money could be garnished on that basis.