In a medium saucepan, heat milk, water, honey, the 3 tablespoons butter, and the salt until warm (105 degree F to 115 degree F). Remove from heat.
In a large bowl, mix the egg on low speed of electric mixer until well beaten. Add the vinegar and beat well. Add the milk mixture and beat well. Beat in the active dry yeast until just combined. Let stand about 5 minutes or until the mixture is foamy.
Add 1 cup of the unbleached flour, the whole-wheat flour, and soy flour. Beat on low speed for 30 seconds, scraping side of bowl constantly. Beat the mixture on high speed for 3 minutes. Using a large spoon, stir in as much of the remaining unbleached flour as you can.
Turn dough out onto a lightly floured surface. Knead in enough of the remaining flour to make a moderately stiff dough that's smooth and elastic (6 to 8 minutes total). Place the dough in a greased bowl; turn once to grease the surface. Cover and let the dough rise in a warm place until doubled (1 to 1-1/2 hours).
Meanwhile, grease two 8x4x2-inch loaf pans with butter. Set aside. Punch dough down. Let rest for 10 minutes. Divide dough in half. Shape each half into a loaf. Place in prepared loaf pans. Cover and let rise in a warm place until doubled (about 1 hour).
Bake in a 375 degree F oven about 45 minutes or until bread sounds hollow when lightly tapped. Immediately remove bread from pans. Cool the bread on wire racks. Makes 2 loaves.
You'll find soy flour in health-food stores.