I don't know exactly when I first learned this term. It could have been in 2013, or it could have been earlier, but certainly not by more than a few years. Probably less than a few years. Anyway, it's something with which I've long been passingly familiar, well before I had any idea what it was called. As Wikipedia will tell you, it's a kind of artificial mix of American English and British Received Pronunciation, which in the 1930s and 40s was associated with upper class American society and the film industry. (It's also sometimes called a "Transatlantic accent." And TV Tropes' page about American Accents includes one folder called "Tidewater/Mid-Atlantic" and another called "The Other Mid-Atlantic," though it seems to me like they're both describing the same thing. But I'm probably wrong. Either way, some of the examples they list under each folder are all things I mean by "Mid-Atlantic accent.")
I also want to mention that the way I discovered the term was probably because I was trying to find out if there was a name for the way announcers spoke in newsreels of that era. And... I'm still not quite sure if "Mid-Atlantic" is what I was looking for, because, while there's a definite similarity, there's a distinctive quality to the accent or inflection of newsreel announcers that has always seemed somewhat different, to me, from people who speak Mid-Atlantic conversationally. It almost sounds to me like a cartoonish parody of a Mid-Atlantic accent. Then again, I may just be thinking of more modern parodies of newsreels, with which I'm much more familiar than the actual newsreels of the 30s and 40s. If I listened to some real newsreels from that era, maybe most (or all) of them would just sound like relatively normal Mid-Atlantic accents. (Or even like newscasters of pretty much any era.)
In any event, this page is probably not going to have any examples of the accent from the era in which it was common. It's mainly intended for later parodies or affectations, whether the characters who use the accent are in a modern setting, or period films set in the 30s-40s, or... any other setting that is attempting to produce a certain feel that is evoked by the accent. (And again, some of the examples I include here will be of a newsreel variety, and some... just how the characters talk.) Anyway, hopefully I'll get around to adding the examples soon. (Some examples I include here can be found on sites such as Wikipedia or TV Tropes, while others I'll add based on my own experience watching TV and movies.) While there are a number of different varieties of Mid-Atlantic accents (Boston Brahmin, Tidewater, Locust Valley Lockjaw, et al.) that I'd like to list under separate headings on this page, for now I'll include all examples in a single list, mainly because I can't always tell for sure which variety a character comes closest to.