Yeah, those were a heavy splinter protection, enough to stop bomb fragments or strafing fighters but not direct bomb hits. The Germans never subscribed so much to the American-style 'all or nothing' armor system, but acknowledged that for stability's sake sometimes you couldn't give everything capital-scale armor. So these mounts weren't overly well-armored- the 5.9-inch mounts, however, were proofed against light cruiser-scale fire (since they were intended for anti-destroyer work, after all).
Marauder has the right of it though, Bismarck's armor was based on Baden, which in turn was based on German assumptions of what WWI naval warfare would look like- by the time that class was going into service Jutland (and to a lesser extent Dogger Bank) had shown that a lot of assumptions were pretty much useless. (Granted, that lesson was learned easier for them than it was for the British! Armor your magazines, dammit!). The result is that while the belt was elephant-hide thick, the deck was surprisingly thin on Baden and again on Bismarck- plunging fire could have been a major problem (which again questions why Lutjens held fire the way he did- it meant that he wasn't fighting back at a point when his ship was at its most vulnerable. Of course, as proven in the Denmark Straight, it was also where Hood was most vulnerable...)
Of course, the real flaw wasn't so much the armor, as iffy as it was, but the lack of any options when it came to the rudders and screws. Bismarck used a strange three-screw system that I've not really seen on most other designs, combined with dual rudders. There was no system to eject the rudders in the event of catastrophic damage to them, nor even really any good access to the system outside of a shipyard- the result was that when the one-in-a-million torpedo actually found home, there weren't many available options- the rudders were jammed, divers couldn't head over the side with explosives to clear them, and even if they had the three-screw system meant it would be much more difficult to maneuver the ship without the bad rudders (by comparison, the Iowa's four screws mean that turning the ship by running one side's props at power and reversing the other side would give her at least some control over the ship, if not an ideal situation. Bismarck would have struggled heavily if it had been an option- as it was, the rudder being jammed meant it was a useless attempt).
Funny, isn't it? If that torpedo hits a meter forward or aft of where it actually hit, Bismarck likely makes it to Brest for repairs, and the war in the Atlantic looks completely different from that point forward. The RAF likely would harass her during repairs, of course, but reunited with Prinz Eugen and with the Scharnhorst and Gneisenau on-hand as well... that's a squadron of ships that could take any convoy's escort and win. Remember that Lutjens prior work to the Bismarck operation was running those two battleships on successful raids during the winter, and the only times he was stymied was due to convoy escorts including old battleships like the Malaya and Resolution. And while they'd still be a threat, they'd also be likely overwhelmed by Bismarck and her friends.
