In a large pot over medium heat add the milk and water, heat just to lukewarm (110°-115°F). Remove from stove.
Mix in sugar and yeast. Whisk until no lumps remain. Add 3 cups of bread flour and salt. Beat until smooth using a wooden spoon or dough whisk. Add the last 2 cups of bread flour. Beat again until combined. The dough should be sticky. Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until indentation remains after poking dough with finger down to second knuckle, about 1 hour.
While dough is rising grate cheese, set aside. Melt margarine or butter and set aside. In a small bowl dissolve baking soda in water, set aside.
Prepare pans: grease two 9x5-inch bread pans.
Stir down dough after it has risen. Stir in cheese, baking soda mixture and melted butter or margarine. Blend well so cheese is evenly distributed. Divide dough between prepared pans.
Cover with plastic wrap that has been sprayed with cooking oil to prevent sticking. Let rise until indentation remains after lightly touching.
Preheat oven to 400°F.
Bake for 25 to 30 minutes. Remove from pans and cool on wire racks.