So your question is an interesting one, and I've been considering how to approach it. The issue is that "a pretty even handed approach to the big picture" is perhaps the last description that one would ascribe to Ambrose. His works are wildly popular pop histories, but generally derided within academic circles, even aside from the whole plagiarism scandal. One of my favorite academically coached putdowns comes from this review of Citizen Soldiers, where the reviewer takes Ambrose to task for his lack of objectivity:

While Ambrose presents an abundance of evidence for the grisly and awful nature of combat-the noise, shock, and feelings of total helplessness and bewilderment that it could induce ("I dreaded going into combat again") - his read on the American war effort is that it was heroic, spectacular, and magnificent. In that sense, his narrative sometimes seems to drift into a form of cheerleading that disconnects from the evidence.

In fact this is something that Ambrose himself practically admits in the epilogue to the book, describing his childhood interactions with veterans, and how he "thought then that these guys were giants. I still do." Which is all to say that Ambrose writes a compelling narrative, and I won't disagree that it is engaging and accessible, but he isn't what I would recommend for an even handed approach to the American experience in Europe during WWII (Sidenote: Rick Atkinson's "Liberation Trilogy" is what I would recommend).

So with that said, I'm making two recommendations for you. If you want engaging, I would recommend Shelby Foote's trilogy "The Civil War: A Narrative". It is quite long, but his prose is simply amazing, so its hard to think of a Civil War book that draws you in more than his. But, the reason I call it comparable to Ambrose here is that it is not very respected academically. Foote was writing in the 50s and 60s, while Civil War historiography was really revolutionized starting in the '70s. Foote represents perhaps the pinnacle of the "traditional narrative". Strong on the "brother against brother" Romanticism of a fractured nation with a subtle dose of Lost Cause influence pepper in to boot. Which is to say, it is great literature, but not always great history.

If you want the even handed approach as well, the most accessible work is Dr. James McPherson's "Battle Cry of Freedom", which is a pretty standard introductory work to an overview of Civil War history. Dr. McPherson is a veritable giant of the field, perhaps the most respected living Civil War scholar even, and you really can't do better than that (he also did an AMA here once!). So if you want something on the Civil War, read that first. Then, if you want to get a bit more literary, get a nice mug of hot cocoa, curl up under a blanket by the fire and read Foote's tome, cause whatever its faults, it is worth reading. It just shouldn't be the first thing you read on the war.

Oh boy...I hate to be "that guy" here, but I need to, I'm afraid. Stephen Ambrose is one of the most reviled names within the professional historian community for a number of reasons (among them, plagiarism accusations, shoddy research methods, assembly line writing methods, unapologetic lying, etc). Ambrose was plagued with accusations of shoddy work (at best) and outright fabrications (at worst) throughout much of career. On several occasions, deeper dives into his sources and the particulars of his work found numerous errors that can only be explained away by half-assed research methods, and/or a complete disregard for honest, diligent leg-work as it concerned fact-checking his info. In some cases (see his "Nothing Like It In the World") he was flat out called on the carpet for lifting huge chunks of other people's work and pawning it off as his own original writing/research.

Is his work accessible, easily digestible, and entertaining? Absolutely...but so is Harry Potter, yet considering Ambrose wrote non-fiction, the fact that his work often operated only just above the same reality level of Rowling's work should give a person a moment of pause. A quick Google search will bring up numerous articles attesting to this sad reality (see here: http://historynewsnetwork.org/article/504 or here: http://utahrails.net/articles/ambrose.php)

If you are looking for Civil War histories that have fantastic peer reviews and a reputation for being both informative and accessible, I'd recommend anything by Bruce Catton (especially his Army of the Potomac trilogy), or James McPherson's "Battle Cry of Freedom" which is very highly regarded on this sub (and rightly so). Doris Kearns Goodwin's "Team of Rivals" is also outstanding if you are looking for a more Lincoln-centered approach.