Heat butter and vegetable oil in a large saucepan over medium heat; add celery, onion, carrot, red pepper, and yellow pepper. Cook and stir until soft and onion is translucent, 7 to 10 minutes.
Stir potatoes, fish stock, and clam juice into the vegetable mixture; simmer for 10 minutes. Stir in corn; simmer until potatoes are tender, about 10 minutes.
Mix salmon, cream, dill, thyme, tarragon, salt, and pepper into the potato mixture; reduce heat to low. Cook and stir until salmon flakes easily with a fork, 5 to 7 minutes. Ladle chowder into bowls; garnish with parsley.