See now this is where I disagree with the "emotional affair" stuff. I have Numerous female friends and I can flirt with them heavily. I am also friends with their husbands. I guess it comes from having 5 sisters it has always been easy for me to talk to women. Luckily my wife is a confident person and see's my relationships for what they are....Friendships. I am a social person, I like people, I talk to thousands of them, my wife is a loner, doesn't like being social...how we ended up with each other, only god knows.
But we are healthy, she knows I would never cheat on her, and never have. But I can go for a drink, have a laugh and even be stupid with my female friends with no worries of "what if" They just know it is fun.
You and your husband need to have a serious talk, figue it out, tell him how you truly feel. Maybe you should hang out with the other couple, meet her husband, have a few drinks together, Have dinner together, or what ever you like to do.
Stop worrying about "what if" worry about "what is" Your husband is reaching out to you, trying to "bring you in" to the relationship, to show you there is nothing to worry about.
I say you go out to dinner and drinks with the lady, let them show you there is nothing to worry about.
I know I am lucky to have a wife that understands I can have relationships with my ex-girl friends, female friends without it being sexual. It is possible, I been married 11 years, dated 7 before that, I never cheated on my wife, I find her the sexiest woman on the planet and she knows it, But I still talk to other women and have friendships with them, they also enjoy me, because they know I am "safe" and back in my younger years, I was the perfect "wing man" for my female friends when a jerk was hitting on them, they would borrow me for a few dances or just join me and my wife (girlfriend at the time) in dancing or a good laugh.
Except he can be friends with other females, BUT you need to be brought into the relationship as well. Until you are fully comfortable with them by themselves.
Some of my best friends are females, they are like sisters to me, but ones i can flirt with.