The only experience I had of someone who was religious Jew denying mental illness (claiming it was a conspiracy of doctors just to make money so they accuse people who have over-imagination of being sick) had a serious mental illness and he himself was hospitalized for a while and now is doing much better though on medication.
The Jewish belief; is that we are all born with certain personalities and tendencies. We all have our good points and bad points and the object of the game of life is to use your traits, mental and physical abilities (whether they are advantages or handicaps) to build a spiritual world in this very physical world. G-d gives us an instruction book (The Torah, talmud etc.) and our own individually designed starting point and it is our job to earn the right to see Godliness everywhere. An extremely difficult task – which is why we are given 120 years or so to accomplish it and some rewards on the way but built in tests and hurdles. Because everyone has a different set of tools to accomplish their task in this world – no one is judged the same or will be successful with the same stories and accomplishments.
Mental illness is a hurdle just like being born down-syndrome or with bad eyesight. Everyone has some kind of barrier sent their way; though some people have much more difficulties. And just like a person who has down-syndrome child or bad eyesight (very different anomalies) it is incumbent on the person/parent to see a doctor and do everything possible to make their lives as healthy as possible. That is part of seeing the Godliness in our physical world; to recognize we are all in need of G-d’s help and need to seek out the right tools that will work specifically for our souls.