Are you sure he's actively "hiding" it? She's not "someone new" (he told you when she was) and she's not "someone significant from his past" (they didn't get that far). Maybe they're just chatting as friends and he thinks it's no big deal.
There's a huge difference between deliberately hiding something and just not realizing it's something that needs to be told. He knew that he already had your approval to talk with her, perhaps he just assumed that was enough?
And how did you find out, anyway? Does your agreement allow for snooping through each other's e-mail?
Gralson: my husband (works out of town).
Auto: my girlfriend (lives with her husband Zoffee).
The most dangerous phrase in the English language is "we've always done it this way."