You shouldn't hear the subs, at all. They should just make your speakers sound enormous, in terms of dynamic range as well as depth. It's hard to tell what you are describing but it sounds like really poor integration.
First, check the placement. Look at the AM Acoustics room mode simulator and try to keep your subs and speakers out of the lowest octaves. Next, measure. Use Room EQ Wizard or OmniMic to see what the response looks like from your listening room. There should be no gaps or excess peaks, but listeners often prefer an elevated shelf below 100 Hz.