The thing is, the addition of either milk or cream will only have your omelet falling apart and looking like scrambled egg. Check out the ingredients and procedure on christinepann.hubpages.com/hub/How-To-Make-a-Perfect-Omelette-The-Quick-and-Easy-Way for an omelet that won't fall apart when you flip.
I used to have the same problem until a chef told me NOT to mix milk with the egg. He said to use a little water and mix with a fork, do not whip the mixture. Make sure your pan and butter are hot before putting the egg mix in and cook on medium heat. It works great.
When you are ready to turn your omelette put your hand under the handle palm up and thumb toward tip of handle. Gently lift handle and slide half of omelette onto plate then go from palm up to quickly palm down. It takes a little practice. Thank Julia for this one!