It is easier to fasten the cross boards to the surface,,, rather than to the ends. (between the posts)
With the boards between the posts, you have a flat plane, onto which to staple/fasten the HC. Attaching the cross boards can be done,,,, but is slightly more challenging, over the placement on the surface of the post.
With the boards placed on surface of post,,,, attaching is simpler, (also stronger in my opinion) but you end up with an uneven plane. Remedy for that,,,, place/attach 2" x2" lumber in-between the horizontal boards onto the posts. (you can also use 2 x 4 lumber if you have supply. I just mentioned 2 x 2 for sake of using less lumber) You end up with a post that is 6 inches thick, allowing you to easily fasten your HC, flush to surface.
Do what you feel you are comfortable constructing.

I can do both methods, but would personally do the horizontal boards placed against the posts. I also am a BIG advocate for using screws.
Hope I made myself clear in explanation. If not, then ask, and I can possibly lay out some lumber and take pictures, and explain that way.
WISHING YOU BEST,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,