Our family of 5 uses a Navigator, but not off road. For the overlanding, I woul dlook into a Expedition (som ehad 3 rows) or maybe a Sequoia/FJ80.
Hmmm. Can't think of anything at the moment...
I've carried 7 people with luggage comfortably (without a thule box on top). You could easily put a thule box on the roof with 6 bikes, and another 4 on a thule rack in back if needed (we often each bring an all mountain and a downhill bike). All in all, its a pretty versatile little rig.
No real budget other then it cant be a new landcruiser or rover, but used is possible. I like the nissan armada , they seem a little more off road ready then the sequia.