Are big banks still safe?

Generally curious what the consensus is on big banks at the moment. Between my husband and I, we have 2 savings accounts, a checking account and 2 CDs through Discover and we each have our own checking accounts - mine is with Chase and his is with Huntington (I think)

I’m starting to get a little paranoid about having more cash stashed away at home but he says everything is fine and it’s better to keep the money in savings to earn interest. Am I just being paranoid? I don’t know what to believe anymore.