I'm pretty much in the position of your bf (except for not being into monogamy at all). I'm biologically male and asexual and happily together with my partner (R., sexual, she's much more into women than into guys), going a tad over four years together now. No sex between us happened in those four years, and none is going to happen in the future either.
I'd consider it more than a bit selfish if your bf, as the asexual partner in a mixed 'ship, would insist on monogamy. I certainly would feel terrible if I cut off R. from living out her sex life; that's not in my place to do, partner or not. I'm certainly entitled to say she can't have sex with me, but that's it - my authority ends right then and there, her sex life with other people basically is not my business but hers, and hers alone. (I'll always be there to talk about it if she wants, offering my perspective and support, so that's not a call for outright DADT; but I do trust that she's a grown up woman who can handle the day-to-day in her relations with others, including their sexual aspects, without me meddling in them.)
If you're unhappy about the prospect of living without sex completely (which, much as I can't personally relate to the feeling, is totally understandable), you two should talk about it... sooner rather than later. Honest communication is key to make any 'ship work - and in your sitch, between partners whose sexual orientations clash, it's even more urgently needed than average. It can work - R. and me show that it can, but I doubt that it can if you're not honest about your needs and wants.
All the best to you!