Melt butter in a large nonstick skillet over medium-high heat.
Stir in mushrooms, and cook until tender, about 5 minutes.
Using a slotted spoon, transfer mushrooms to plate.
Remove skillet from heat.
In a small bowl, beat egg yolks and milk to blend.
In a separate bowl, beat egg whites with a dry beater until soft peaks form.
Fold yolk mixture into whites.
Return skillet to medium-high heat.
When butter sizzles, pour egg mixture into skillet.
Sprinkle mushrooms and crabmeat evenly over the top.
Cook until omelet begins to set, about 3 minutes.
Sprinkle with Swiss cheese.
Using a large spatula, fold omelet over, forming semicircle.
Cover skillet; cook until omelet puffs and is cooked through, about 3 minutes.
Slide omelet onto large plate.