I consult with an overseas psychologist via Skype. My current BCBS health insurance pays 80% when I visit my US psychologist. I don't know how to make the international health insurance since this is non emergency. How can I get reimbursed, even though in part, for my international psychologist sessions?
Base on your comments that your insurance does cover these types of visits, and they do have an out-of-network coverage you might have a chance of getting them covered.
Keep in mind that out-of-network coverage doesn't work the same way as in-network coverage. They will have separate deductibles, they will only credit you for the maximum benefit they would have paid for the session if you had gone in-network. Many out-of-network doctors will not submit paperwork to your insurance company, meaning that you will have to handle all the paperwork.
You will need to call the insurance company. You should do this before the first session. They will need to prove to their auditors that the bill you submit is legitimate. Of course you could just risk it, and provide all the paperwork you have after the first session, and then use the time before the second session to appeal their decision if they reject it.
Regarding language. Is it possible to find a US based doctor with the same language skills? Since you are going out-of-network anyway, and you are willing to do it via Skype, isn't it possible that there is some doctor in the US that speaks your language.