Preheat the grill to high. Whisk 1/4 cup vinegar, 3 tablespoons oil, garlic, 2 teaspoons each juice and mustard, and a pinch each of salt and pepper. Place asparagus and mushrooms in a zip-top plastic bag with half of dressing; marinate 15 minutes. Grill asparagus 5 minutes. Grill mushrooms, gill sides down, for 4 minutes; turn. Grill 7 more minutes. Slice thickly. Toss greens with vegetables and dressing. Serve warm.