I have been working out and running, often on the same day but not right after one or the other. I do long distance usually about 2 miles. I am wondering that by doing this I could be burning the muscle that I build by going to the gym, is this true?

All depends on your calorie intake and what you eat and your training goals. I frequently will run 5 miles or more and do a two body part workout right after my cardio. I have never had trouble developing muscle although the amount of size you gain will be less w/ this approach.

I don't think 2 miles is enough to affect muscle mass unless you are extremely lean. I work out 3 says a week and run 3 days, alternately, and I haven't notice any such issues. I have fatigue problems sometimes, since extra rest seems more critical going 6 days and I know I get too little sleep. My routes are 3 to 3 1/2 miles and I am over 40. A younger athlete might not have the same fatigue problems unless they went substantialy longer distances. I think you will be fine. The running is a nice break from the weights. I go outside weather permitting as I am not a big treadmill fan.