If the smoked cod has a strong smoky flavour, soak it in water for 30 minutes, drain and rinse.
In a large saucepan, cover the cod and smoked cod with water and add the juice of half a lemon and the thyme. Bring the cooking liquid to a gentle simmer. Poach the fish for 8 to 10 minutes, or until the fish is just cooked and tender. Remove the fish to a bowl and reserve the poaching liquid. When the fish has cooled enough to handle, break it into large bite-sized pieces. Set aside.
While the cod is cooking, peel the parsnips and cut them into 5mm slices. Peel the potatoes, cut them into 1cm dice and place them in a bowl of water to prevent discolouring.
In a large saucepan, melt 2 tablespoons of butter or margarine over medium heat. Add onion and cook until wilted and golden. Add the parsnips, potatoes and 3 cups of the reserved poaching liquid. Bring the mixture to a boil, reduce heat and cover. Simmer for 15 minutes, or until the vegetables are tender.
Heat the milk and cream in a small saucepan. Do not boil. Stir into the vegetable mixture.
Add cod and smoked cod; stir. Season with salt and freshly ground pepper to taste. Just before serving, stir in remaining tablespoon of butter. Top each serving with freshly ground pepper and chives.