Place cinnamon sticks, allspice berries, and cloves in an 8-inch square piece of cheesecloth. Gather edges and tie with kitchen twine to make a sachet. Add sachet, cranberries, and orange juice to a large saucepan. Bring to a boil over high heat and cook until cranberries burst (about 10 minutes).

Stir in apples, pears, white sugar, and brown sugar. Return to a boil, reduce heat to medium-low, and simmer until apples and pears are slightly soft (about 25 minutes). Remove spice sachet.