There is a free script at:
http://www.mp2kmag.com/importersub01.asp
It will work best if you have some programming skills to modify and recompile the code if errors crop up with your data. This will only take the drawing layer (i.e. shapes, lines, and points you have drawn) and convert them to a mif/mid. It will not extract the MapPoint built-in layers such as roads.
MIAB puts the built-in layers as a raster image into MapInfo automatically. You can imagine doing this yourself, just register the map image. MIAB makes it much easier.
Eric