Preheat oven to 350 degrees F (175 degrees C). Cut a 1-inch thick slice from the top of round bread loaf; hollow out the loaf to use as a bread bowl. Slice the cut-off top of the loaf into cubes for dipping. Combine cream cheese, Cheddar cheese, ham, green onion, and chives in a microwave-safe bowl. Heat in microwave on high power for about 15 seconds to warm ingredients for easier stirring. Spoon cheese mixture into prepared bread bowl; place on a baking sheet. Bake filled bread bowl in the preheated oven, stirring occasionally, until bread bowl is toasted and dip is bubbling, about 30 minutes. Serve with Italian bread cubes for dipping.