I don't know about group family plans. I know that children are covered by their parents' insurance at no extra cost as long as they live at home.
I have a private health insurance that covers me worldwide except in Germany. Coverage is 100% (propyhlactic, treatment, emergency treatment, hospital cost, medication, oversea transportation, body recovery and transport; dental coverage is about 95% for prophylatic and simple fillings, about 70% for crowns etc). I pay about $190 a month. My insurer is AXA.