"It was supernatural power that Jesus exercised when He turned water to wine, but the result was not supernatural wine. It was regular wine." - Wilson, AC, p132.
When we are born again, we do not become "heavenly" beings or supernatural beings. We become real humans, sons of the new humanity. It is a supernatural act, but we are still regular humans, albeit transformed, or rather, adopted into a new family with a new Father and a new destiny.