In Pennsylvania, I-80 (along its entire length), I-81 (along its most of its length, the exceptions being south of Carlisle and between Harrisburg and I-78), I-70 (south/east of the PA Turnpike), I-84 (along its entire length), I-380 (along its entire length), and US 322 (between the Lewistown narrows and the Susquehanna River–technically not an interstate but built to interstate standards of the time in that area) have long lengths of tree-filled, wide, variable-width median. I guess you could say that the majority of PA interstates and interstate-grade highways are like this. So like froggie said, it's not just Virginia.
The one great exception to the variable-width median in PA is of course the PA Turnpike, which except for a few locations features a narrow, constant-width median along its entire length, both main trunk and Northeast Extension.
A lot of the forested mileage features median that was left at or near original grade, either higher or lower than the roadway, so you often have duel cuts with trees towering between the opposing carriageways. Especially dramatic is where there are tall cuts beside a very high median with trees atop. In some spots, like I-99 through the Steam Valley area and some locations on I-81 in central PA, opposing carriageways are on opposite sides of a dramatic valley.
I love the variable-width, forested medians. I find they produce the largest variety of scenery and views while I'm driving, which helps to decrease the likelihood of so-called highway narcosis. I also think it's just plain more fun to drive.