I think your best bet that will cover everything from the 1760s - 2000, other than the gap between the Civil War and the Depression, due to the volumes not being published yet, is the Oxford History of the United States. It gives an excellent overview of the political, cultural, and military history of the United States. It's pretty long, since the volumes are typically 700-1000 pages and there are 8 published volumes, with 4 still in the works, but they're pretty easy to get through, especially if you're interested in history (why else would you be reading them?). The individual volumes have won and been nominated for numerous awards including the Pulitzer and Bancroft prizes.

Like I mentioned, the two volumes between the Civil War and the Depression have yet to be published, as have the two volumes that will cover everything from Columbus until the 1760s. Hopefully, we'll see those in the next few years. As it stands, the other volumes are well worth reading now, even with the gap.

On the whole, I'd say the series is unbiased. I do hear some people level claims of bias against the final two volumes (covering 1945-2000), but that might also be due to their proximity in time and when you say something negative about a President like Polk, people don't have emotional attachments. When you say something negative about someone like Kennedy or Reagan, people get upset. Even taking that into account, I'd say they're about as unbiased as you could hope for.