Heritability of "mental illness"

There's an interesting thing people say/think about the prospect of having kids in a family where someone was known to have a serious "mental illness". They say, "Aren't you worried that your kids will be [insert mental illness name here]"?

People think that "mental illness" runs in families and that it's the genes that are doing the carrying. They think that some people have genes that make them more likely to get some "mental illnesses" and some people don't have those problematic genes.

I do think that genes allow for this stuff, but instead of it being a scenario where some humans have it and some humans don't, I think it's a scenario where some species have it and some species don't. The human species has it and the rest don't.

So regarding heritability, it's memes doing the carrying, not genes.