I mean, was this normal back then?
No, this was not normal, and a civilian airship of any kind would never have a aircraft, especially a military one stored underneath.
That is not to say however, that it did not happen.
In the early 20th century, many nations did begin to experiment with "parasite aircraft" and so-called airborne aircraft carriers, which were just airships outfitted with several parasite aircraft.
These aircraft were intended to be used for reconnaissance, self defence, or offense against raiding zeppelins, however I am unsure if they were ever actually used in combat situations, as the two carriers were built by the US in the inter war period, and the other experiments, largely by Britain and Germany, were scrapped, despite being successful.
If you want more info, you should check out these links, which can give you some more basic information, and point you to further sources or relevant topics.
http://en.wikipedia.org/wiki/Airborne_aircraft_carrier
http://www.airships.net/us-navy-rigid-airships/uss-akron-macon