For what it is worth, I’m not having any problems accessing my router
Windows 7 Pro, 64 bit. Avast 2014.9.0.2008 VD 131112-1
Internet Explorer 10
(Enhanced protection mode off)
AOS (4 modules) Enabled)

It may be the difference in OS, or in IE version, however suggest you could check:-
(a) That your router address is correct
(b) Disable all of the AOS modules in IE11

What version of Avast are you using?