Per DoDI 1322.29 active duty service members are not eligible to receive wages, training stipends, or any other form of financial compensation for the duration of your internship. This does not include reimbursements to offset living expenses or work-related travel expenses.
You will continue to receive all pay and benefits from the DOD. Since you will be on PTDY/PTAD for your internship, if you currently receive BAH, you will continue to receive it at the same rate.