You've got some troubleshooting to do.
First: Make sure that your battery switch is wired correctly. Download new installation diagrams from the manufacturer if you don't still have the ones that came with the new switch. Don't assume that just because the old switch was wired that way, that it was ever correct or that the new one needs to be wired the same way. If you have a multimeter, check to see if you have voltage/continuity at the output terminal of the switch when it's off; it's unlikely but possible you got a bad switch.
Second: Check your battery terminals. Make sure you know exactly what each connection on the positive posts of your batteries goes to. If you've got voltage bypassing the switch (and the switch is working correctly), it has to be coming from something that's energized from the battery. You might have two positive wires that are chafed through and making contact, so that power is being fed from one circuit to another. If the problem is constant (i.e. the "house" power stays on all the time, and not intermittently) and you can rule out the switch, you could start pulling terminals off the batteries one at a time. When the house electronics lose power, you've found the circuit that's feeding them.
Third (you should do this anyway): Start digging into your electrical system. It's worth it to know where everything goes and what it does.
Does everything on your house circuit have power when the switch is off, or just some items or sub-panels (switch panel, fuse panel, etc.)? If it's just a couple things... definitely need to trace wiring and see where they're wired to get power from. If it's all the circuits, you need to know where that wiring feeding the fuse block and/or switch panel is going.
I admittedly just started doing this with my 2530 (should have done it years ago). I'm ASTOUNDED by how poorly this thing is wired. Lots of shortcuts, very little attention to detail, lots of "one size fits all" work (which it never does). If I wasn't replacing most of it anyway, I'd definitely reworking it. I can't fathom how we haven't had major electrical issues yet, given the state of the electrical system. Truly disappointing to see from Parker, albeit a mid-90's boat.
In your case, my money is on a mis-wired/malfunctioning switch. But if there's damage to the wiring somewhere that's transferring voltage, that's something that you need to find out about ASAP.