In a large mixing bowl combine milk, honey, and yeast, stirring until yeast dissolves. Let stand for 5 minutes. Meanwhile, grease an 8x4x2-inch loaf pan; set pan aside.
Add flour, egg, oil, and salt to yeast mixture. Beat with an electric mixer on low speed until combined. Beat for 3 minutes on high speed, scraping side of bowl occasionally. Using a wooden spoon, stir in whole wheat flour and oats until combined. Spoon batter into prepared loaf pan, spreading evenly. Cover; let dough rise in a warm place until double in size (about 45 minutes).
Preheat oven to 350°F. Bake about 40 minutes or until bread sounds hollow when lightly tapped. If necessary to prevent overbrowning, cover top of bread with foil for the last 10 to 15 minutes of baking. Immediately remove bread from pan. Cool on a wire rack.