In a large soup pot heat butter, olive oil, onions, mushrooms, garlic and ¼ teaspoon salt; sauté on medium heat for 7 minutes.
Add remaining ¼ teaspoon salt, carrots, celery, herbs, chicken and chicken broth. Bring to a boil and then lower to a simmer, cover pot, and cook for 20 minutes.
Add cooked wild rice, Swiss chard, white wine (if using) and whole milk. Simmer for an additional 2 minutes and serve.