Well, working off of a word that is probably more well known -- "semi-annually" -- which means twice a year, it would seem to indicate that semi-monthly would mean twice a month, and bi-monthly would then mean every other month. That's the way I learned it, too -- Miriam notwithstanding.

I also work for attorneys, and they must fulfill "x" number of Continuing Legal Education (CLE) hours per two-year period (known as a biennium). So since a biennium (or bi-annually) means every other year, ditto for bi-monthly -- every other month. As one other example, a bi-monthly newsletter is sent every other month.

And yes, we do have a screwy language -- ask any non-English speaking person who has had to learn our language.

CaT
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If future generations are to remember us with gratitude rather than contempt, we must leave them more than the miracle of technology. We must leave them a glimpse of the world as it was in the beginning, not just after we got through with it.
- Lyndon Johnson, on signing the Wilderness Act into law (1964)