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No, it is you who will pay less tax because you are the one filing. He owes no tax because his income is exempt.

You will be filing either Married Filing Separately or Head of Household depending...

One more thing. If you wish to claim the spousal exemption the spouse must obtain a ITIN.

See other threads for the Form W-7 and process.

If you file OTHER than Married filing jointly you may still claim the spousal exemption. See sec. 151(b) as below

(a) Allowance of deductions
In the case of an individual, the exemptions...

Told by whom?

If you file jointly you must obtain an ITIN and then elect to be treated as a US resident for tax purposes under sec. 6013(h); goodbye exempt tax status.

He can still claim the...

Look, your spouse is getting all his income tax free. Figure the tax on his income and then figure what you are losing by filing MFS.

I believe you will find that you come out ahead by filing as I...

Just so ATE, my fault for not mentioning that.

Your husband's income is exempt from tax under sec. 893 of the IRS Code. He is considered a nonresident alien.
Thus, you will file as Married Filing Separately. Because of this filing status you may...