In multi-bank devices such as JL-J, it is indeed possible to read from one bank while another bank is being erased or programmed.
If a program command is issued to Bank 1 when Bank 2 is busy erasing, the command will be ignored. The device supports Erase Suspend and Resume function. You can suspend the erase in Bank 2 first, then program in Bank 1. After the program is done, you can resume the erase in Bank 2. This can be easily implemented in software.