Although the stats page has a nice little pie chart, is there some way to work out exactly how much time you have played as each class...?
Yes there is.
Multiplayer > Leaderboards > Jump to Leaderboard > [Insert Kit Here]
Multiplayer > Leaderboards > Kit > [Insert Kit Here]
You can also do very similar for vehicles.
note that time spent in vehicles is not included in these class stats for some bizarre crazy reason. Time spent in a vehicle is "classless" Jan 23, 2012 at 23:16
1You could also go to your award screen and select the (kit) service medal and check your progress towards it if you're feeling daring.– Emerica.Feb 1, 2012 at 15:00