I'm not a post processing guru by any means, but I do fiddle around a bit with Lightroom and have discovered the Tone Curve (or Curves Tool in Photoshop) can be incredibly powerful. I was able to successful adjust the tone curve in Lightroom to achieve a very similar result.
But first, I don't think the green in these photos was intentionally highlighted, it just happens to be about the only non-neutral colour in the images. To achieve the same effect, the most important thing to do is get the right composure, and that's all done outside of photoshop, in the real world.
Once you've captured an image in the style of those above, you'd need to make some minor curve adjustments to wash out the blacks and shadows. Adjust the curve as demonstrated in the picture I've attached.
From there you can fiddle around with the curve a bit more, I felt the following curve had the best effect:
The idea is to flatten out the curve on the highlights side - this ensures you don't loose too much contrast. But of course, it depends on what you're going for.
I hope this helps - Like I said, I'm kind of new to post processing, so I'm keen to see how others answer your question. I would bet there is more than one way to achieve the same results!