In my experience, it doesn't matter if the segment is your originating segment, or a continuing onward segment, as long as one segment in the leg for which you are checking in is in FC. You can check three bags free of charge.

If no segment in the leg is in FC, then you can only check two bags free of charge. It doesn't matter if other legs of your reservation contain FC segments. Of course, you might be lucky and get an accomodating agent.