I also had the same problem, even after lowering all settings I was still only seeing around 15 fps on average in multiplayer while easily getting over 60 fps in single player on very high settings. This is the same thing that would happen in Arma 2s multiplayer as well... but I haven't yet had a chance to try that game out again since I installed my new 670 ftw the other day so maybe that game will run better now.
I managed to make the arma 3 multiplayer a bit more playable by trying a suggestion I found in another thread somewhere on here. I opened the config file "C:\Users\"username"\Documents\Arma 3 Alpha\arma3alpha.cfg" and changed the line GPU_MaxFramesAhead=1000; to GPU_MaxFramesAhead=1;. This seemed to knock the average frames I was getting straight up into the 30s and sometimes 40s with a mix of standard/high settings in multiplayer. Not exactly a fix by any stretch of the imagination but an improvement nonetheless.