I have the same problem in my 2000 ssei. I have an alpine headunit with aftermarket pioneer 6.5" door speakers in the front and the rest are the stock bose speakers, but everytime i get the volume over 10 the sound shuts off to the interior speakers but my subs keep hittin. i'm pretty sure what is happening is that your overloading the amp built in to the head unit and its causing it to shut down...try getting a 4 channel amp.

The problem is the impedance of your speakers. Stock speakers usually are 8ohms or more. This allows cheaper factory head units to use a two channel amp and a speaker level fader to split power between two speakers (or more) on the same channel (front and rear). The new head unit has four dedicated amplifier channels meant to run at 4ohms (just like aftermarket speakers). What this does to the head unit'* amplifiers is it reduces the output by 1/3 (maybe more). You are over driving the head unit, trying to drive higher impedance speakers to achieve the volume that is expected out of them. The only way to rectify your problem is to purchase aftermarket speakers that are 4ohm.