The cough in and of itself is not an MG symptom. However, if your husband experiences dysphagia, or difficulty swallowing, the cough could indeed be indicative of some problems with MG. If he is aspirating saliva or fluids, he very well could be coughing it up, mixed with the mucus you describe.

If this is what you feel might be happening, I would urge you to call your doctor. Aspiration can become a serious complication.