Did you set your preferences in Adobe Reader to open the file in a separate (Adobe) window or is it opened in the browser window? That's a different value for that setting, and a different behaviour. One of them might be what you want.
If no luck, try Foxit or Nitro reader as an alternative for Adobe Reader. The last time I installed Foxit it wanted to install the Ask toolbar in my browser, so mind the checkboxes when installing!
I had always been able to open pdf documents on website until I downloaded Adobe Reader 11. Now I have to save them first. I took this up with Adobe direct and got nowhere. What I get is a white cross in a small black box in the top left corner of the screen.
I have sometimes a similar problem with viewing pictures via Windows Explorer, although not with Firefox.
I am running Windows 7 on a PC.