Even more - 64 per cent - said they would resist going to hospital because of concern for their child, and almost half do not have a care plan for their child if they become unwell or need medical help, the study found.
The survey of 330 parents with a mental illness found only about a third had told their child's school they had a mental illness, and half of these found the disclosure unhelpful, leading to stigmatising and in some cases, bullying of their child.
"It is unacceptable that in 2012, people are too embarrassed to say they have a mental illness," said SANE Australia chief executive Jack Heath.
"Not only is this unfair to the parent, it is also unfair to their child, whose health and education can suffer as a result."
Most of the survey participants were women, and the most common diagnosis was depression (50 per cent), followed by bipolar disorder (23 per cent).
Just under half the participants lived in rural areas.
Schizophrenia sufferer and single mum Kylie Griffin and she had to move her two daughters to another school because of the teacher's attitude when she informed the school of her mental illness.
"Saying that you have a mental illness should start the discussion, not shut it down," she said.
SANE Australia recommends better sharing of information about on-the-ground support for parents with mental health and their children, and that schools review policies and practices to help families where a parent has a mental illness.
For further information on SANE Australia, visit: http://www.sane.org/
Information and advice is also available by calling the SANE Helpline on 1800 18 SANE (7263)