Is there a chance factor of psychiatric patients passing on the disease to their off-springs?

Yes. We know that many psychiatric problems have an increased genetic risk. However, this is not guaranteed to occur. Even though the risk is increased for many disorders, the chances are still greater that a problem will not be "passed on" to the next generation. It is good to be aware of the possibility, but to not automatically expect it to occur.
Genetics. Chances increase if both parents have the illness or it is chromosomal dominant.