In a medium saucepan over medium, melt the butter. Add the thyme, parsley, and salt, and let lightly simmer for a few minutes to incorporate the flavor.
Meanwhile, peel and chop the turnip, and remove the woody stems from the asparagus.
Lay vegetables on a sheet pan, and spoon half the butter mixture on top. Mix, then place in oven for 20 minutes.
Remove the pan from the oven, and lay the fish over the veggies. Spoon the remaining butter mixture over the fish and veggies. Bake for another 20 minutes, or until the fish is done.