When you say he only growls when you pet another dog, what I hear is I'm the alpha and there is no room for anyone but me. This is unacceptable behavior. If you want to pet another dog you should be able to. The fact that you can't should tell you your dog is in need of training help. It is the don't pet another dog today but it may be stay away from children or I don't want visitors at my house or some other attitude later if you don't get it under control now. The fact that you have a mix of two naturally more dominant breeds also is more cause for concern. This mix is going to require a strong alpha human to let the dog know who the pack leader is and what will be tolerated.

Again... Best of Luck I'm sure you love him dearly and only want what is best for him