Cream together the butter, shortening, and sugars. Add the vanilla, salt and vinegar and mix together. Beat in the egg, then the baking soda and flour. Stir in the chocolate chips.
In a different bowl, mix the cream cheese with the sugar until thoroughly combined. Beat in the egg and vanilla.
In a greased 9x13 pan, spread half of the cookie dough mixture across the bottom. (I just plopped the dough around the pan and then spread it all together.) Then, spread the cream cheese mixture on top of the cookie dough.
With the remaining cookie dough, flatten chunks of dough between your hands into discs, and then place on top of the cream cheese mixture. (The cookie dough discs don't have to touch, but try to place them so that they cover as much of the cream cheese mixture as possible.)
Bake at 350 for 35-45 minutes, or until the top is brown and cooked through. Cool completely and store in the refrigerator.
Serve and enjoy!