My husband is working for a US company overseas. Is any of his income exempt from Federal Taxes?

Maybe. US Citizens are taxed on their worldwide income. They do get credit for foreign income taxes paid and a foreign income exclusion. You or your husband should consult with a tax adviser to give you more comprehensive information about how to handle your situation than you can get here.
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Go to IRS.gov and download IRS publication 54. Pay attention to form 2555, the housing exclusion and form 1116. The foreign earned income exclusion requires that the taxpayer be physically in other countries (non-countries like Antartica or working on an oil rig do not count) for 330 days out of a 365 day period. If the time is met, up to $85,700 could be excluded. (If he left in June and returned the following June, you would prorate the exclusion.) Even if you meet the test for the exclusion, any other income is taxed as if the exclusion wasn't being used. (The exclusion knocks out your lowest tax brackets first.) The foreign tax credit works on averages and can be used with or without the foreign earned income credit.