The technical term for these widely-separated roadways is "bifurcated highway." When they were first built in VA (around 1970 more or less) they were thought to be a great advance in safety.
Bifurcate means "to divide or fork into two branches." Not that I'm in any way an arbiter of road-related terminology, but I use the term bifurcation to refer to a temporary increase, for aesthetic or engineering reasons, in the width of a median that's otherwise of a typical, lesser width. In most cases, the standard width was sixty feet or thereabouts (64 in my own state) during the heyday of Interstate construction. I think that every state has them, though policies toward how long, wide, frequent and degree to which the alignments of the two carriageways differ seem to vary between various states.
But what the OP is referring to, I think, is the adoption of a standard median width that's very large, 90 to 150 feet, enough to allow for the preexisting forests to be undisturbed by construction (even if the trees end up being cut down for whatever reason!). Virginia is one of several states that did this. Another is Tennessee, which... I'm fascinated with I-24 between Chattanooga and Nashville, so I did some checking on Google Earth and found that:
Headed northwest from the bottom of the Monteagle grade, the highway was built in 1963 or so. The median is 60 feet for the first several miles, but then goes to 100. The newest sections, c. 1968 or so, have a standard width of 120 feet. Through Manchester and Murfreesboro and one pass through a ridge the median drops back to sixty feet, but within the 100 and 120-foot parts are further bifurcations of up to 200 feet! There's a significant section of ninety-foot median as well, where there's a good bit of lateral slope across the right-of-way.
When forming my opinions as to the awesomeness of the various state highway systems, apparent policy toward median width and bifurcations is definitely a factor. Regardless of their actual merit, wide medians are luxurious, and that impresses me. Variety counts for a lot with me, too, and that's one of the things I like best about Tennessee compared to any other state I know reasonably well.