Cream white sugar, brown sugar, butter, and shortening together. Beat in eggs one at a time, until well combined. Add milk, and vanilla; beat well.
Combine dry ingredients--white flour, wheat flour, salt, baking soda, oatmeal, and chips--and add to wet ingredients; mix well.
Drop dough by rounded tablespoonfuls onto ungreased cookie sheets. (Refrigerate dough between batches.)
Bake at 375°F for 8-9 minutes for a chewy cookie or 10-12 minutes for a crisp cookie. Cool 1 minute on cookie sheets; remove to wire rack. Cool completely. Store tightly covered.