Is ic hereditary?

Yes. There is a tendency for i.C. To recur in families, siblings and daughters. There is also a family tendency for endometriosis and these two problems often run together. I am not aware of the exact gene problem linked to this difficult problem.
No. Ic is not hereditary, although, offspring of parents who suffer from ic is definitely at a higher risk for acquiring it, so there may be genetic predisposition but no definite recessive/dominant transmission.