When diarrhea is evacuated from ones anus while they are vommiting. Barfarrhea is caused because when a person wretches they involuntarily squeeze their bowel muscles used to clear the colon as hard as they can.
Barfarrhea is likely to occur when one suffers from food poisening.
I was barfing into the toilet and a puddle of diarrhea was under me when I finished.
I was going diarrhea and I had to vommit on top of my feet.