I'm obviously not rejecting materialism, I'm merely attempting to distinguish between "mental" and "physical", i.e., the cause of your 'mental illness' is "nutrient deficiency" vs. "your wife left you". If, on balance, people experience mental distress when they experience extreme emotional turmoil without any significant accompanying physical event, we can't posit a physical cause and therefore shouldn't seek a purely physical solution (drugs).
People have 'mental illness' because of mental problems, not physical problems.
Also: everything has some genetic component, this is trivially true. Genetics are what separates humans from dogs and plants. It doesn't necessarily help us to explain the phenomenon adequately.
Also also: another way science works is its inability to prove negatives. Therefore, saying, "someday we might discover this" can be said for pretty much anything that remains unproven.
I suspect I don't understand exactly what you are distinguishing here.
If your identical twin has schizophrenia, there is a 48% chance that you will have it too. This is compared to the chance of the general population, which is something like 1%. This feels like something is physically wrong in those who are schizophrenic. I don't know how else you would get that kind of result.
Yes, twin studies have often been trumpeted to demonstrate that schizophrenia has a strong genetic basis. However, we've yet to find any actual genetic variation strongly associated with schizophrenia, which, with such a high rate of concordance, should be a snap. Twin studies themselves are suspect in a number of ways - the assumption of environmental equivalence between twins and the general population is suspect, for example. Fraternal twins also show higher concordance than siblings, even though their genetics should be the same.