That's an oxymoron, IMO, but that's a whole different discussion.
I would expect the more "orthodox" Jewish parents to send their kids to Hebrew schools, for the same reasons that faithful Catholic parents who don't homeschool SHOULD send their kids to Catholic Schools. Still, I'm aware of Protestant, Jewish, mohammedan, Buddhist, and Hindu children in Catholic schools.
My mother broke the trend. She was a teacher and I was the first to not attend catholic school. I thank God every day for her decision. The schools on Long Island were and are fantastic. I sent my kid to public schools as well.