Its not easy hiding mental illness from the world; its even harder to hide it from family, and especially children. Instead of avoiding talking about it with children, or being fearful of the effects on them, parents should be able to get help. Unfortunately, there are limited resources available to deal specifically with this situation.
There is a program that provides parenting training to mentally ill parents, as well as a support group for parents which are discussed in the article, but there aren't many other places parents can turn. Therapists don't often address the roles people play as parents or the way things may affect other members of their family, and so this shortcoming in treatment is in need of attention.