To clean the mussels, put them in a large bowl and cover with water and soak for 30 minutes, or until the mussels are free of any sand. Drain the mussels, then remove the "beard" from each one. If they're dirty, scrub the mussels under running water. Discard any dead mussels, mussels with broken shells or shells which are not tightly shut.
In a large non-aluminum stockpot, heat the butter and olive oil over medium heat. Add the onions and cook for 5 minutes; then add the garlic and cook for 3 more minutes, or until they are translucent. Add the parsley, wine, salt, and pepper. Bring to a boil.
Add the mussels, stir well, then cover the pot, and cook over medium heat for 8 to 10 minutes, until all the mussels are opened (discard any that do not open). Pour the mussels and the sauce into a large shallow bowl and serve hot.
Notes
For spicy mussels: add 1 tsp of dried crushed red pepper and simmer when you add the wine and parsley.