My husband had the money order made payable to the Internal Revenue Service instead of the United States Treasury. Will our payment be processed correctly?

Yes, it sounds like your check will still be cashed. From the IRS link below:

Checks and money orders should be made payable to "United States Treasury." Checks and money orders made payable to "Internal Revenue Service" , "U.S. Treasury" , or "Department of The Treasury" can still be accepted and processed. Checks and money orders made payable to "IRS" or left blank must be over stamped with "United States Treasury" immediately upon receipt. If the check or money order is made payable to the taxpayer, the taxpayer must endorse the check or money order. If the taxpayer is not available to endorse the check or money order, the check or money order must be returned to the taxpayer.

See here: 

https://www.irs.gov/irm/part21/irm_21-003-004r-cont01.html