Is it normal to be blamed for somebody being depressed?

I personally do not find that normal at all. It is NOT your fault what mental problems SHE has. Isn't this some kind of emotional abuse, too? It's most definitely not your fault, unless you've murdered a few people then that might cause her some emotional distress. I'm sorry, hon ):

That is an awful thing to suggest to your own child. She obviously has unresolved issues and should be seeking help instead of placing the blame on you. Try not to take it too personally and maybe suggest that she talk to someone.

maybe she's just conflict with herself about things and looking for an outlet for all the negative emotions, it's not normal to blame another person for depression, usually people who are depressed blame themselves for everything but it's pretty common for people who suffer from it to take it out on other people. maybe just let her know you're there and you care about her, might not fix things but it could help her to feel a bit better over time

Hell no! Your mom is just looking for someone to blame for the foolishness she's doing when she's popping them pills! Try to get her some help before she sinks deeper into it. Whenever she plays the ''blame game'' try and don't let it get to you and just remember that she needs serious help. Trust me once she gets professional help and they get to the root of the problem all of the days where she's blaming you will be over! Good luck