I covered biennial or biannually quite a while ago now, but Guy K Haas commented on my index to all of these Troublesome Pairs that I should cover bimonthly or semimonthly, and biweekly or semiweekly. And so I shall.
However, one caveat before we begin: Try not to use these. There is so much confusion about words like these, that it is almost always so much better to write “Every two weeks” or “Twice a week” rather than using the more complex term. After all, these terms are usually used when one is scheduling something, and you don’t want your scheduling to go awry, do you!
Bimonthly actually means, in the dictionary (all of them), taking place or appearing twice a month … or every two months. So that’s no use, is it!
We find the same issue with biweekly – it can mean either (both) taking place or appearing twice a week … or every two weeks. Useless, again!
Moving on, semi-monthly and semi-weekly do mean occurring or appearing twice a month / twice a week (and notice that hyphen: that’s a bit annoying in itself, isn’t it!).
So, my recommendation: leave these well alone. State the exact times the whatever it is will be doing whatever it does. “My magazine is going to come out every two months” – “Oh, mine’s coming out twice a month, or every two weeks”. Job done.