In large microwavable bowl, mix cream cheese and 1 cup of the Swiss cheese. Microwave uncovered on High 1 minute, stirring after 30 seconds, until softened and cheese is starting to melt; add additional 30-second intervals as needed. Beat in milk with whisk until mostly smooth; mixture may still be slightly lumpy.
Separate dough into 8 biscuits; cut each into sixths. Gently stir into cream cheese mixture; stir in chicken and ham. Spoon into baking dish. Top with remaining 1 cup cheese.