Preheat oven to 425°F. Sift flours, sugar, baking powder, baking soda and salt into a large bowl. Add butter and use your fingertips or a pastry cutter to work butter into flour until no pieces larger than peas remain. Stir in chives and buttermilk, stirring just until mixed.
Turn dough out onto a lightly floured surface, gather it into a ball and knead once or twice, just until it holds together. Press down on dough until it is about 1/3-inch thick. Cut little biscuits out with a round 1 1/2-inch cutter. Place biscuits on an ungreased baking sheet. Press scraps together and cut out more biscuits. Brush tops of biscuits with milk and bake until biscuits are golden, 10 to 12 minutes.
While biscuits are still warm, split them and fill with ham.
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