Combine 3-1/2 cups flour, undissolved yeast and salt in a large mixing bowl. Heat water, milk, honey and oil until very warm (120o to 130oF). Gradually add to flour mixture; beat 2 minutes at medium speed with electric mixer, scraping bowl occasionally. Add 1 cup flour and wheat bran; beat 2 minutes at high speed, scraping bowl occasionally. With spoon, stir in enough remaining flour to make soft dough.
Knead on lightly floured surface until smooth and elastic, about 6 to 8 minutes. Cover dough and let rest 10 minutes.
Divide dough in half. Roll each half to 12 x 7-inch rectangle. Beginning at short end of each rectangle, roll up tightly as for jelly roll. Pinch seams and ends to seal. Place, seam sides down, in 2 greased 8-1/2 x 4-1/2-inch loaf pans. Cover; let rise in warm, draft-free place until doubled in size, about 30 to 60 minutes.
Bake in preheated 375oF oven for 35 to 45 minutes or until done. Remove from pans; let cool on wire racks. (Note: to test for doneness, internal temperature of bread should register 190oF in center of loaf.)