It seems to me that you would need more information about what your partner and his in-town lover have agreed on as far as what they will or won't share with each other. Whatever their level of disclosure is to each other, I think that *you* need a greater amount of disclosure from *him.* Maybe it's not what he wants, but it's what you want. You'll need to start looking for some kind of area of compromise.
If his in-town lover truly doesn't want to know about his other relationships, then that is her preference and right. Don't press the issue if that's their agreement, but first you need to know whether it *is* their agreement. In other words, you need him to tell you more about what's going on with her. Then you'll have a better understanding about where you stand, and what the dilemma before you really looks like. Right now you just have some vague information that she "trusts" him, without any idea of what she trusts him to do or not do. You need to find out. You need details.
He seems to want to compartmentalize his relationships as much as possible, so I wouldn't be surprised if he resists your efforts to find out more. He seems to be very "Don't Ask, Don't Tell." You are an open book. You need him to open his book a little (a lot?) more. Seek a time and opportunity to bring this up with him.
Depending on how willing he is to work with you on opening up the disclosure channels, you may have a decision to make as to whether this is the level of communication you can live with and be happy with for the long haul. If all this "mystery relationships" (He has a relationship with her, but I don't know what kind of relationship, and he won't say) gets to be too much, then for your own sanity you should consider cutting your losses and letting him go.
On the other hand, maybe he'll start opening up more about that in-town relationship, and if he does, that's great. To me, the current level of DADT is probably unhealthy. But I'm not close enough to the situation to know. I don't know what his reasons, rationalizations, and justifications are.
For some people, DADT seems to work. But I don't think it's working so well for you. Just my opinion based on what is presented.
I hope you will be able to come to an amicable solution.
Love means never having to say, "Put down that meat cleaver!"