What receiver are you currently using? Have you tried testing different receivers? Some tuners have better equalizer logic which can make a big difference in how well they deal with multipath interference (there's a brief technical discussion about equalizers in this post:
http://forum.tvfool.com/showthread.php?p=365#post365).
An outdoor antenna and/or a more directional antenna setup are expected to do better for your current situation because it cuts down on the amount of multipath that your tuner has to deal with. Most of us would expect to see at least some improvement in the situation when you move the antenna outside, even if it doesn't completely solve the problem. A tighter antenna pattern (better antenna or stacked antennas) should improve the situation even more.