I have a friend who wants to learn more American and European history. She is not interested in military stuff (although obviously wars would be a part of any history she does not want something that dwells on just that or individual battles and so on). It does not need to be one book on both. Can be two books, one on each topic.
I realize whole books can be written on a single aspect of history (WWII, the Depression, Civil Rights and so on). More looking for a good overview.
Preferably the thing will read well and not be like a textbook. Something that would interest most people and not be so dry as to only enthuse another historian.
The answer to all your one-volume history needs (especially when there’s nothing more in the OP than “Europe and America!”):
J.M. Roberts: Penguin History of the World..
Has a bit more in it than America and Europe, but, you know, there’s also a bit more than that out there, so…
For American history I like Paul Johnson’s A History of the American People. Johnson is British and a conservative, so there is some controversy about his perspective, but as a liberal I found his book comprehensive and interesting to read, and didn’t feel that it was overly biased.
Howard Zinn’s A People’s History of the United States. History from a different point of view than what we usually see (Natives, Blacks, women, workers, etc.).
Norman Davies’ Europe: A History. Somewhat controversial, but a very good read.