Can my wages be garished for a hospital bill that's for my husband,?

In many states, spouses can be held liable for debts incurred by the other spouse under the "doctrine of necessaries (or necessities--both terms are used interchangeably)" that applies to such things as food, clothing, shelter and in many cases medical care. There may or may not be a legal basis for the hospital to get a judgment against you, but if they are garnishing they either have a judgment (which you may or may not be able to have vacated), or the hospital is a public one and there is an administrative route for them to get paid which obviates the need for them to go to court.

You need a Tennessee attorney to tell you all the ins and outs. I will tell you that Tennessee is one of the easiest states for creditors to garnish in. Consequently Tennessee bankruptcies are rather high on a per capita basis.