This is cool!
Everybody has a Jewish date for their birthday. If I have the general date (complete with year, of course, seeing as the dates change every year), I can find the Hebrew date.
A friend of mine says that the whole time between her general-date birthday and her Jewish-date birthday should be dedicated for celebrations. It's mostly a couple of days to a couple of weeks, but sometimes it can be nearly as long as a month, and in rare cases, the dates coincide again.
On official forms then you just write what? For example when you filled out a visa request for the US, what did you write on the form?
The general date, if that's the only option.
If there's room, not just boxes to mark and the like, I try to fit the Jewish date as well, on principle, because that's the date that matters to me. But in most cases, there isn't any room for that.