In a large mixing bowl, combine the warm water, milk, honey, and yeast. Allow the mixture to sit for about 5 minutes until slightly foamy if using active dry yeast.
Add the soft butter, salt, and whole wheat flour. Stir until a soft dough forms.
If using a stand mixer, place the dough in the bowl fitted with the dough hook attachment and knead for about 6 to 8 minutes. The dough should become smooth and slightly elastic. If mixing by hand, knead the dough on a lightly floured surface for about 8 to 10 minutes.
Place the dough in a lightly greased mixing bowl and cover with a towel. Let it rise in a warm place for about 60 minutes, or until doubled in size. Once dough has risen, turn the dough onto a lightly floured surface and divide it into 12 equal pieces.
Shape each piece into a round dinner roll and place them in a greased 9x13-inch baking dish.
Cover and allow the wheat rolls to rise again for about 30 to 40 minutes.
Preheat the oven to 375°F. Then, bake the whole wheat dinner rolls for 18 to 22 minutes, or until the tops are golden brown.
Brush the rolls with melted butter while they are still warm.