Is bleeding through your mouth during a nosebleed normal?

I am not quite sure, I have googled it but the answers were not quite certain and pretty vague. It was during a shower when I started having a nosebleed, then started coughing up blood. I did hold my head back, but after that bleeding subsided I had a next bleed, but this time I didn't hold my head back and coughed blood. Is this bad?