After some more research yesterday night, I think I found the solution to my problem:
As mentioned Verisign is using an intermediate certificate. You can find more information on the topic, if searching for "chained certificates". The solution is not only to have your own private certificate in the crt file, but also the intermediate. These are just plain text files, which can be copied-and-pasted in a text editor. Important here is the order, first the private, than the intermediate. After this things are working fine.
