Welcome to the forum.
Imported into a proper AVCHD Project, those MTS files (if they are full AVCHD) should be editable, and then you can Export/Share to many, many formats.
As "AVI" is but a "wrapper," and can contain all sorts of material, I would check out that program, to find out which CODEC's it wants, in the AVI wrapper. Let us know that little bit of info, and someone can go beyond my rec. "it should work fine," with a definitive answer.