Is it normal if you're currently on the pill and you have missed two periods and you're now bleeding very heavily?

It depends, did you just start the pill? If you just started the pill that is not uncommon due to your body adjusting to the hormones. There are so many things that can effect periods from stress, change in diet. To be one the safe side I would give the doctor a call and see what they have to say. Good Luck. I suggest you go to the doctor immediately, heavy bleeding is never normal.