I don't know if it'd work if your husband is against being among groups of people, but what about attending gatherings that your kids can enjoy while whoever your husband met online can get to know you and your husband a bit without it being so centered on her that you have to worry about the kids getting attached to her after just a couple visits?
Friday night I was at a poly gathering at a big cafe with an outdoor courtyard with about 40 adults and a couple people had brought their kids along. With the large space the kids were able to just run around and entertain themselves for about an hour, just checking in with their dad every 10 minutes or so, while he got a chance to talk to people. If your husband were meeting someone from online, it wouldn't even need to be a poly gathering, just an event where the new person wouldn't stand out too much from everyone else in the kids' mind.
I've met several people I've dated online, and generally try to transition to seeing them in person as quickly as possible to make sure any feelings generated are reflective of reality, and also so they can meet the other people in my life early on.
Last edited by turtleHeart; 07-08-2012 at 04:35 AM.