Avoid biweekly altogether. Use fortnightly for "once every two weeks", and twice a week for, well, "twice a week".
Not everything has to be a single word, so don't be afraid to use more than one word when you want to use clear, understandable, unambiguous language.
If they have problems with fortnightly, use every other week, or let them into a little secret: fortnight comes from "fourteen nights", or two weeks.
Edit: From the comments it's clear many Americans won't understand or are uncomfortable with fortnight so, to be safe, use the aforementioned every other week.
Best Answer
It was done once. It was done twice. It was done never. It was never done.