Want the the truth only from what I've seen in a number of cases?
Happy he might be, but rarely if he's faithful. Faithful he might be, but not necessarily happy. The majority of times this sort of relationship requires an honest approach towards an arrangement of some sort, giving him the freedom to fulfill his other needs, or he will resort to doing it privately, (to not use the term sneak around behind your back).
You have to ask yourself lots of tough questions point blank and proceed from your most brutally honest answers to yourself. You are the one that needs to see wether you would be happy in any eventuality, but don't expect him to change and don't lie to yourselves, please!

Yes they can, I happen to be a bi-sexual b/f and my girlfriend is also bi-sexual, but I am a very happy and faithful boyfriend to her. My policy is look but dont touch, like I would always point out the hot guys and she would agree, and we would fantasize about a 3some with another guy but its all cool. We have been steady for 3 months now and it has just been nothing short of perfect.