What does biweekly mean to you? How about bimonthly or biannually?
While each of us will have our own, perhaps unambiguous, reaction to it, the word biweekly is interpreted as "twice a week" or "once every two weeks." I know this from personal experience of confusing people en-masse. The dictionary even carefully, if unhelpfully, defines it as meaning either. It's a strange quirk of the English language. But it's so handy, what to do? An excellent concise solution is the word fortnightly.
Fortnightly has the helpful unambiguous quality that it means "once every fortnight," so "once every two weeks." And it's also just one word. If something happens "two times a week," I think you need to spell it out or use "twice a week" or perhaps "every Monday and Thursday."
The same source of confusion applies to the words bimonthly and biannually—to be sure of being understood correctly, it's best to avoid them. Phrases like "every second month," "every two months," "twice a month," or "two times each year" are helpful here.