I'm bisexual and I understand where you're coming from OP.
When you can play for either team, restricting yourself to one gender feels like a loss of sorts. Sexuality is a form of expression and for a bisexual to commit to one gender feels a bit ... stifling.
(Perhaps this is why I'm 42 and terminally single).
If a threesome now and again would help scratch that itch, then I'd say go for it -- your H sounds like he's excited yet terrified by the prospect.
But if your relationship is built on a firm foundation of trust, the experience would probably make you stronger.
You need to make sure that you don't fall for any of your 'third spoke' bed-partners. That way lies nothing but trouble.
Of course, not all bisexuality is 50/50. You can be gayer than you are straight, or vice-versa. If you are secretly gayer than straight, then perhaps you ought to be reassessing your original relationship, rather than dabbling in threesomes, because it will all end in tears.
In summary: Tread boldly but with care.