I do not wear a wedding band with it but you could go either way; I probably would not put it on the wedding band since I wouldn''t care about it spinning. BGD made mine and it does not spin, my diamond is never on the backside and it''s very comfortable.
I have a euroshank on mine and I do not wear it with a wedding band. However, I think that if you wanted to do the e-shank on the e-ring there is nothing saying how the band has to be. However, if I wore a band, I would want it to be a perfect circle; just my preference for the band. So I would go with a plain band.
I love my e-shank ring. It does not spin around and stays in place. I wear my rings a little big, too.