This question has been answered by BobRay. See the first response.
Does each group have a different role? If so you shouldn't have to since role are inherited AFAIK.
Roles are only inherited within a user group, not between user groups. Actually, I recommend giving everyone the same role to avoid confusion, since most of the time, the only function of roles is to give users in the same group different rights and I think it's less confusing if you use separate groups for separate sets of permissions.
Some version of this might also work: http://bobsguides.com/blog.html/2013/05/22/protecting-pages-the-easy-way/.