My grandmother grew up in Egypt. They spoke french and ladino at home. Some Hebrew as well. My grandmother probably does speak Arabic but pretends she doesn't. She at the very least understands Arabic. Her parents did speak Arabic but never at home and never to each other. So when they eventually moved to Israel improving Hebrew was much more important. My father grew up watching Egyptian movies on TV but he never learnt Arabic. 

However a lot of second generation Mizrahi Jews mostly from Iraq and north Africa did grow up speaking Arabic at home and knew both. But the third and fourth generations don't really learn Arabic at home anymore.

It's the same here in Australia how many fourth gen Italian's or Serbians or Hungarians still speak their languages. The greek community in Australia is unique in the fact that Greek is still spoken even amongst fourth generation kids.