When I married my husband less than a year ago, he had incurred (as a
single man) a $30,000 tax bill that he is currently paying off at a
rate of $300 a month. Now that we are married will the IRS consider
this a debt that BOTH of us owe?

Caveat: I am a Canadian NOT familiar with US tax law...the answer
below is STRICTLY from searching the net and is NOT guaranteed.  My
advice would be consult a tax accountant.

Link:  http://www.unclefed.com/AuthorsRow/GretaHicks/myths.html
Question
If I marry someone who owes the IRS money, that is a separate property
debt and I do not have to pay it.
Answer
STOP! If you live in or move to one of nine community property states.
The day you get married all income becomes community property income
which is loosely defined to mean one-half of your income is hers and
one-half of her income is yours. If the debt remains unpaid, the IRS
can levy (take) one-half your paycheck to pay for the old separate
property tax bill. Or, if you later file a joint income tax return and
you are due a refund, the IRS can keep the refund to pay towards the
old debt.

You can protect your money by a "buyer be aware" attitude. 

Before marriage, make sure all income tax returns are filed and paid. 
Have a credit check run or go to the court house and do a lien search
to see if the IRS has filed any tax liens.
A pre-marital agreement designating your income as separate income
does not fully protect you but it is better than nothing. You'll need
to contact an attorney to discuss further this protective measure.

also see:

http://www.unclefed.com/GAOReports/ggd98-72t_sum.html

http://64.233.167.104/search?q=cache:WTaMCrqV9FIJ:www.irs.gov/pub/irs-pdf/p3512.pdf+innocent+spouse&hl=en