You must file Form 2106. There are reasons why one of your employers taxed your per diem. It has nothing to do with you but the accounting plan that they are using to pay per diem. Such plans are called nonqualified plans by the IRS. (From these plans, they cannot reimburse you tax-free. They must tax it, and then you can claim the deduction on your tax return). Form 2106 is how. This FAQ shows you how to access this form in TurboTax: https://ttlc.intuit.com/replies/4800418
How you will need to enter the information into TurboTax is this: You enter in all of your per diem expenses (what you are entitled to receive), and then later you enter the amount of per diem you were reimbursed with tax-free money. This will determine the amount of per diem (and other qualifying expenses) that are potentially deductible.
The reason they are potentially deductible is that you must have more expenses than 2% of your AGI, and then be able to itemize deductions. While it is not a guarantee that you will get anything extra back on your tax return, this is the way to correctly report your situation to the IRS.
For information on the 2% rule, please see this FAQ: https://ttlc.intuit.com/replies/4800344
Daniel: This is vague: "You enter what you are entitled to receive". I hope you don't use that statement often. I don't think you are knowledgeable enough on the subject to give advice. My ACTUAL experience is that first of all you need a record of how much you actually spent on food lodging etc. Then you said "enter the amount of per diem you were reimbursed with tax-free money". They specifically said their per diem was taxed. It's hard to believe you are an employee tax expert.