Can a married man have a single lady friend at work outside of marriage?

My husband and I share the same group of friends (male and female). We have no friends outside of our marriage, so I thought. We have always been open and honest about things. I love my husband dearly but his recent actions are making my eyebrows rise.I recently found out that my husband has a female friend at work that he exchanged numbers with. I found out about it through phone records along with how many times and the times of day and night they talk, depending on what shift he's on. She has texted him at 5am saying "Mornin Pooh-Bear" and also texted on a couple of occions to ask if he was either at work or home. I addressed my husband about this friendship IMMEDIATELY and my concerns. He says that is strictly platonic and she is just a friend. It amazes me because they only talk during working hours. They never talk once he's home. I'm trying to figure at what point did it go from co-worker to friendship status, especially when he has never mentioned her to me. I have texted her from his phone asking her to stop. I even called her back from his phone (which she picked up) to tell her to cease communication; however, she hung up on me when she heard my voice. She knows that I am not fond of this.She then started calling fromm an "unknown" number for him to her right back (which I also showed him in our phone records) thinking I wouldn't notice. This is when I got livid. Knowing he's was in hot water with this situation, he tried to make arrangements for me to meet her when I dropped him off to work, which didn't fall through. He claimed that she went on vacation and he didn't know. I still haven't met her yet to this day and he dosen't bring it up. It's simply swept under the rug. My husband works at night mainly and sometimes days. He claims that the friend is an old lady (mother-figure) at work who goes around giving hugs and nicknames. Thats still inappropriate for a married man. She hasn't been calling because he knows that I am able to see it through phone records; however, when he came home from work the other day there was a text from her. She had text him "Good morning" and provided him with her work extentsion so he could call from worklines. I truly believe they have never stopped commumicating. He ereased his texts before he gets home so that all that is available are texts from me or guy friends. I believe this day he simply forgot. Also, this woman name and number is not progammed in his phone. So to ensure that he knew that I saw the text, I stored her cell number, and work number into the phone under the name "Pooh Bear" so the next time she calls or texts he will know that I am aware, which I'm sure has already happened and he's not coming forward. Both of their actions makes it impossible for me to beleive that they are "just friends" and that she is an old lady. He says he didn't come forward with it in the begining because of how I may react. Proabably no different from the way he would if the shoe was on the other foot. Should I be alarmed? Am I being disrespected by both because they both know; however, she can only do what he allows? What should I do?