Preheat the oven to 350°F Coat baking sheet with cooking spray.
To Make the Schnitzel:
Whisk the milk and egg together in a large bowl. Spread the breadcrumbs on a large plate. Dip the mushroom and eggplant slices into the milk mixture, then coat the slices with breadcrumbs. Shake off the excess crumbs, and place on the prepared baking sheet. Spray the vegetables with cooking spray(or you may brush with some olive oil), and bake 10 minutes. Flip vegetables, and spray again with the cooking spray(or more olive oil). Bake 10-15 minutes more, or until the vegetables are tender and breadcrumbs are dark golden brown. Set aside.
To make Lemon Caper Sauce:
Melt the butter in a saucepan over medium high heat. Cook 2-3 minutes, or until the butter begins to brown. Stir in oil and capers, and cook 1 minute more. Remove from the heat, and add lemon juice and parsley.
To serve, stack 1 mushroom and several eggplant rounds on each plate; drizzle with the lemon caper sauce,and garnish with lemon slices and parsley sprigs. Serve immediately. Enjoy!