Let there be no confusion; bimonthly means every two months and same goes for biweekly.
Sorry for droping in so late. Rgds.

There is no ambiguity in respect of the meaning of “biannual”.”Biannual” means “TWICE per year”, that is, “TWO TIMES per year”. NOW THAT WE HAVE ESTABLISHED A PLATFORM OF AGREEMENT, let us proceed.
We are correct: The prefix, “bi-”, means “two” OR “twice”(depending on the sense of its usage).

Originally/classically, “bi-monthly” was ascribed the meaning, “occurring TWO TIMES per MONTH” or “occurring TWICE per MONTH”. This was not to have been confused with “SEMI-monthly”, which means, “occurring once every HALF-month”.
Follow me closely now. If events, P and Q, occurred on March 27, 2009 and March 28, 2009, respectively, then they occurred TWICE PER MONTH, but P and Q would not have occurred SEMI-monthly, since the interval between the occurrences of the two events was NOT HALF of a month. Hence, “semi-monthly events” ARE “bi-monthly events”; but “bi-monthly events” are NOT NECESSARILY “semi-monthly events”.

Ah. You are still with me. Beautiful.

Finally, because language is dynamic and the meaning of a “word” is arbitrary, the meaning ascribed to a word may change, depending on widespread its use is deemed to be. Lexicographers, therefore, later agreed that BECAUSE OF THE WIDESPREAD, POPULAR DEVIATION IN USAGE FROM THE CLASSICAL MEANING OF “BI-MONTHLY”, THE SUBSEQUENT (mis)USAGE WHICH MEANS “occurring ONCE every TWO MONTHS” SHOULD BE EMBRACED.

CONCLUSION: “Bi-monthly”, originally meant “occurring TWO TIMES per MONTH”;
“Bi-monthly” was later also taken to mean “occurring ONCE every TWO
MONTHS” because of popular deviation from the original meaning.

However, semi-monthly may hold a stronger argument for that position, as semi- implies less than the suffix.

Finding it amusing that the vote is barely in favor of ‘twice a month’, even though most of the common sense arguments in the comments would point to ‘every two months’.