Have you tried to take the vitamin with food?
Me, I split my "One A Day" type vitamin/mineral pill into two and take one half with breakfast and lunch. I avoid dinner for minerals to give any excess the best chance of getting excreted during the day when I'm pushing a lot more water though my kidneys.
As for your problem ... are you sure that's not just some dye in the pill? I don't know of anything that would be "bright green" that you'd likely be taking.
If vitamins get fully absorbed why is my piss bright green when I take a multivitamin?