In a large bowl combine flour, cocoa, baking powder, baking soda, and salt. Set aside.
In a bowl of a stand or hand mixer with a paddle attachment, beat butter until smooth. Gradually add sugars and beat until blended and a little fluffy. (This should take about 2-3 minutes)
Add eggs one at a time until mixed in. Add the flour mixture alternating with the milk/lemon juice. (Begin and end with the flour mixture, and remember to scrap downs the sides of the bowl so that it is all incorporated). Beat until smooth. Mix in chocolate chips. (Not optional. Chocolate chips are a must.)
Fill the Bundt. Spoon about a third of the mixture into the bundt tin. Pour in all of the cream cheese mixture. Then spoon in the rest of the chocolate cake batter. The chocolate cake batter is heavier so some of it may collapse into the cream cheese. Don't worry…it will turn out ok.
Bake in the oven for 1hr 10min-1hr 20mins. this may depend on the oven. The top (which is really the bottom!) should firm to touch. When you skewer the cake, the chocolate should feel firm and not wobbly but the skewer may come out a little chocolatey because of the moist cheese inside.
Allow the bundt to cool completely. Be patient. When cool, cover the cake with a plate, flip the bundt upside down (or is that right-side-up?). Once inverted, lift away the bundt tin.