Place the whole wheat flour and white flour in a large bowl and stir to combine. Set aside.
Heat the milk in a saucepan over medium heat until it almost boils. Turn off the heat and let the milk cool in the pan. Place the water, oil, honey, eggs, salt, and yeast in the bowl in an electric mixer and blend. When the milk has cooled to the touch, pour it into the bowl with the yeast mixture and combine briefly on low. Add the mixture of flours, blending on low to combine well. Remove the beater and add a dough hook to the mixer if you have one. Beat for 5 minutes on medium speed. Or, turn the dough out on to a lightly floured surface and knead with floured hands for 5 minutes. It may still be a little sticky.
Mist a large glass bowl with vegetable oil spray and turn the dough into the bowl. Cover with a kitchen towel and place in a warm place to double in size, about 1 to 1 1/4 hours. Punch down the dough and turn out onto a lightly floured surface and knead until smooth, 3 to 4 minutes. Add 1/4 cup flour if needed to bring the dough together so it looses its stickiness. Divide the dough in half and shape each half into a loaf, and place into 2 greased 9-inch loaf pans. Cover with the kitchen towel and let the dough rise until doubled, about 45 minutes to 1 hour.
Place the pans in a cold oven, and heat the oven to 350 degrees. Bake until the loaves are deeply browned, and the top is hard when tapped, about 45 to 50 minutes.
Remove the pans from the pan, run a knife around the edges, and invert the loaves into a rack to cool on their sides. Slice and serve.