Place the potatoes and parsnips in a medium pot. Cover with cold water. Add 1 teaspoon salt and bring to a boil. Reduce heat and simmer until tender, 15 to 20 minutes.
Meanwhile, in a small saucepan, over medium heat, heat the cream, milk, and butter.
Drain the potatoes and parsnips and return to the pot. Add the cream mixture and 1/2 teaspoon salt and mash. Transfer to a serving bowl.