In a heavy saucepan, combine the berries, apple juice, water, sugar, lemon juice and nutmeg. Cook, uncovered, over low heat for 20 minutes or until berries are softened. Strain, reserving juice. Press berry mixture through a fine meshed sieve; discard seeds. Add pulp to reserved juice; cover and refrigerate until chilled.
Place berry mixture in a food processor or blender; add yogurt. Cover and process until smooth. Pour into bowls.