How likely is for the children to inherit mental illness from the parents?

It depends upon the nature of the parental illness. If a parent is genetically insane or unbalanced the trait will be present in the offspring. Although it still may not present itself. If the parent has suffered a mental trauma such as a nervous breakdown there will be no inherited effect. Dysfunctional is not a mental illness per se.

If the mental illness is organic, there may be a genetic component. Dysfunction (I spelled it correctly, you didn't) is a behavioral, rather than a biological, issue, and thus is not "inherited" per se, but can certainly be repeated since dysfunction is typically a result of ignorance and poor choices.

You don't "inherit" mental illness, but it seems that way. Reason is, you learn the same social dysfunctions and are exposed to them, as your parents. It does tend to "inherit" to kids.

There isn't a quantifiable equation to give you an exact likelihood, all we can go on is statistical data.We know is that they are more likely to develop dysfunctional behavior patterns.