They are the massive high-voltage long-distance transmission lines. As Sandlizrd eluded to, they seem like they sag pretty damn low. I'll try to get a better estimate next time I ride, but they can't be any higher than 25-30 feet above the road. I rode under them again this morning without getting zapped, but I was keeping my legs away from the frame. They make rather unnerving loud crackling sounds when you ride under them.
And yes, the amount of protection any rubber will afford you depends on the thickness of the rubber and the voltage. We used rubber mats and thick gloves when I was a power plant electrician. Then again, I never worked on transmission lines with hundreds of thousands of volts.