Going back to some of the first super-heroes in comics, there was an implicit understanding that the readers were a mixed bag. There was always humour to be found, for those that looked for it. It was probably Captain Marvel's ability to appeal to different sensibilities--kids took everything seriously, adults saw how funny this all was--which accounts for his huge success. Even then this wasn't new, since comic strips had done the same sort of thing for a long time (Li'l Abner being a good example).
While all those zany Batman stories in the 50s and early 60s were played straight, it was understood that college age readers and parents would be reading these books, in addition to the main audience of kids, and where the kids saw Batman as a serious character, the older readers understood the silly aspects of the stories.
Even when you get Silver Age characters that are supposed to be more serious--like The Flash or Spider-Man--the writers are clearly throwing in a lot of things that their older readers can laugh at. It confuses me that today's readers miss this. They take John Broome and Stan Lee too seriously--and when something silly happens in a story, they assume this is a flaw in the writing. No comic book writer took super-heroes absolutely seriously, because they all understood that the premise was inherently ridiculous. There's no contradiction in providing great entertainment and adventure through absurd characters.
The producers of the Batman TV show understood this facet of comic book characters and saw that as their hook. They foregrounded the silliness--which is what makes it camp--but just like Captain Marvel, they played everything straight. Which is what makes it even funnier (but a difficult balancing act--I think as the show went on they overplayed their hand). In point of fact, by this time Julius Schwartz was trying to downplay some of the absurd elements (no Bat-Mite or extraneous Batman family members, more night time scenes and mystery), so the TV show threw a monkey wrench into the works. The comic book had to play both sides of the fence--because they had to satisfy the different expectations of their readership.
Still, as a kid picking up Batman comics for the first time because of the TV show, I didn't see a huge difference between the comic and the TV show. There were a lot of little niggling details between comic book, TV show, comic strip, trading cards, and the reprints that appeared in the 80 page Giants. But I could live with those small differences--it was all essentially the same Batman (and no, the origin of Batman was not played up in the 50s and 60s in any medium). Other TV shows and movies have been far less faithful to the original source material. Only the 1970s Wonder Woman, in its pilot episode seemed more faithful in my opinion--but then it was being faithful to the original Sensation Comics no. 1 story, rather than the Wonder Woman comics of the day.
In the end, because it was a fad and people can turn on fads with great venom, Batmania suffered its own Batarang effect. The boom became a bust. Although I'd argue that comic book publishers across the board benefitted from this renewed interest that the TV show sparked. It didn't just become a fad to buy Batman comics. It became a fad to buy any comics--and comic book symbolism became a part of the pop art culture in the late 60s. It's quite possible that the comic book industry would have been in a much poorer position in the late 1960s, if not for the bounce it got from Batmania. However, Batman became the main victim of the bust--but that itself was not an absolutely bad thing, since it gave Schwartz the opportunity to make further changes to Batman (changes which many embraced--of course, if you loved the old Batman this wasn't the best result). And the brief success of Batmania in the mid-60s gave the Batman movie in 1989 a ready made recognition that fueled its own Batmania success.