Yup, they'll definitely both be on the same ring main.
Assuming it is a ground loop that's causing the problem, one of these beauties
will see you straight. They're possibly the most used things in my box of audio tricks here.
One other thing to watch out for, however good your motherboard is the onboard sound will be, quite frankly, crap. You'll always get a bit of said interference just because of its nature - the solution is really just to buy a sound card and use that instead.