Preheat oven to 400 degrees and spray a baking sheet with nonstick spray.
In a small bowl, whisk together 2 tablespoons olive oil, butter, honey, brown sugar, Dijon, garlic, oregano and basil; season with salt and pepper, to taste. Set aside.
Place potatoes in a single layer on the baking sheet. Drizzle with remaining 1 tablespoon olive oil and season with salt and pepper, to taste.
Place chicken on top of potatoes and brush each chicken breast with honey mixture.
Place into oven and roast until the chicken is completely cooked through and the potatoes are nearly done about 25-30 minutes.
Stir in broccoli and green beans during the last 10 minutes of cooking time. Cook until tender-crisp and cooked through.