Is it true that Islamic banks deal with usurious banks within the same system, and therefore it is forbidden to deal with them?

The key in dealing with banks lies in the extent of their adherence to Sharia (definition) controls in their financial transactions. If a bank observes these controls, there is no objection to dealing with it or working for it. As for the necessity for Islamic banks to deal with interest-based banks in some cases, such as dealing with the central bank, this does not prevent dealing with them or working for them in what is permissible.