This does not sound like a situation that requires using interrupts. Using interrupts introduces several issues and makes the solution more complex - my advice for interrupts is to use them only when absolutely necessary and then only reluctantly and as little as possible.
In this case what you need to do is design your sketch to use a non-blocking approach, which means it can control several activities concurrently and independently. "Non-blocking" means that you code does not stop (block) to wait for time to pass or an outside event to occur before doing something - instead the code tests for all the events which are relevant to it and handles them as they arise. The 'blink without delay' example sketch is the simplest demonstration of this approach. See Robin2's sample code posted recently for a more complicated and realistic example.