Hitler was baptized as an infant into the Roman Catholic Church, which was the official church in Austria-Hungary, where he grew up. But I don’t know of any evidence that he ever showed any commitment to Christian doctrine as an adult; his membership in the Catholic Church was purely nominal, and he did not participate in the sacraments.
The “Christianity” that Hitler occasionally affirmed in public was one that most Christians would not recognize because it was “Nazified.”
The Wikipedia article on this topic has many citations to give you an idea of the conflicting interpretations of Hitler’s religious views: http://en.wikipedia.org/wiki/Religious_views_of_Adolf_Hitler
As to the role of religion in the Nazi state, Hitler tried with some success to turn the churches into instruments of Nazi policy. He succeeded to the extent that the leadership of the churches echoed nationalist propaganda when the war started. However, there was always resistance within the churches, too.
I don’t know as much about Goebbels, unfortunately, but I hope this helps.