Bi-weekly/semi-weekly
For part of my career at Hewlett-Packard, we had meetings with our boss. These periodic meetings were held every two weeks. At times, discussions ensued about whether these meetings were bi-weekly or semi-weekly. ( Semi-monthly , for that matter.)
Here is some insight to help you decide which term is correct. The prefix bi means two and semi means half.
With this in mind, bi-weekly means every other week (every two weeks.) Semi-weekly would mean twice in a week–Once in each half of the week.
With that in mind, I guess our bi-weekly meetings were also semi-monthly meetings. I guess I would go with calling it an every two weeks meeting if I had to do it again.
Now you know.
Exploring the use, misuse and humor of words 
In some months, your bi-weekly meetings would be more frequent than semi-monthly. For example, if your meetings were held on Tuesdays or Wednesdays in January 2013, you could have had three bi-weekly meetings.
Good point Gene. Thanks for pointing that out.