I have kept in contact with some of mine and my brothers childhood friends. We usually communicate by email and basically ask the same type of questions. How is your mom? How are your brother and sister? Hows the weather in Denver, CO? Thanks for sending us some snow to Arkansas! Etc!!! He went to college to be a Meteorologist and was for a few years. He has a perfect voice for doing radio commercials and was moved to that field of work. He makes good money and is still single with 5 basset hounds. Most likely will never marry. My husband has never been jealous and I forward or show my husband every email we pass back and forth.
On the other hand, I also have an uncle who is always texting me about family matters and then turning them into sexual comments. I ignore most text from him and if I want to know how my Grandmother and everyone is in Louisiana, I call a different uncle or aunt to get the information. My Grandmother does not have a phone. I only communicate with him if I can't get a hold of anyone else and I cut the conversation when the sexual comments began.
My husband also keeps up with former coworkers from his department both male and female by email. He usually forwards to me the entire conversation by email. I know all of these coworkers and do not feel threatened at all by their communication.
It sounds as if you husband is not keeping it from you and is trying to make sure that you know exactly what conversations they are having. I would suggest that you make an effort to meet her along with your husband and just see for yourself if there is anything to worry about. I do not suggest interfering unless there is a reasonable cause.
Also, you must remember, that texting is quickly become the primary way of communication and calling people is quickly going out. Also, with texting you know what is being said in their conversations. With a phone call received when you are not with him leaves you with only what he wants you to know if he bothers to tell you.