If I have an employee that is temporarily based out of the country for a period of 2 -3 months and they are paid a per diem for their living expenses (hotel, food, travel, etc.), while still having to maintain their home, car, etc. in the U.S. does the per diem qualify as taxable income or is it considered a reimburseable expense?

It is considered non-taxable reimbursement IF it is an ACCOUNTABLE plan, meaning the employee has to submit expenses reports to get the per diem. If he is paid per diem without such expenses reports, it is a NON-accountable plan and would probably be considered taxable.

Yes, it depends upon how your employer reports this on your W-2.
If employer reports this as income, which I doubt, you can claim these expenses as itemized deductions on form 2106.