I have three kids here in Budapest. I am English and the mother is Hungarian. All three (aged 8, 5 & 2) are bilingual, though verbally, not in written English, yet. My eldest loves reading in Hungarian and can read in English despite not having had formal teaching to do so.
"Proper" school doesn't start here until kids are 7, but they acquire formal language skills pretty quickly once they do start.
One great advantage, for them, is that my Hungarian is dire. They know they can't speak to me in Hungarian, so they don't try. Kids take the path of least resistance linguistically, in my expereince. We get British TV here to reinforce the message and an annual Blighty trip helps too. When on a playground in England, the other kids just assume that my brood are English.
I have ex-pat colleagues who can speak the lingo here much better than me, and their kids tend to be weaker in English, because of the path of least resistance thing.
When I lived in Sweden, my boss & his partner were Scots/Australian and American respectively. They had a child and only spoke Swedish to it. Rather stupid, IMO, but in keeping with his management skills...