Looks like interlacing to me. Play with the deinterlacing settings, including the mode - better deinterlacing needs more CPU grunt, so that may be a problem on a Pi, but perhaps the Pi2 is up to it.
You could always run a sample through Handbrake and force the frame interpolation there so it become a progressive image, and then test that if you want to see proof. But odds on it's because it's not deinterlacing, or not doing it properly.
EDIT
Quick recording from BBC ONE HD on Freeview, PCTV290e (so your stick's predecessor).
Playback through VLC - with no deinterlacing:
http://s22.postimg.org/4lx0bi91d/interlace_1.png
With deinterlacing set to 'auto', mode = 'Bob'
http://s28.postimg.org/e1vg5qezx/interlace_2.png