A married female coworker texted my husband:
Hi how are you feeling? Are you sleeping any better?
My husband texts back:
No but it's okay . I miss you though
She text:
Be glad to talk if it helps! Not until after 13 th
He text:
Sounds good

Sounds like they're friends.

If he showed you the texts then obviously there's nothing to worry about. :)

So what is your question/concern?

So tell him to stop it, personally my wife would have taken my phone and stomped on it.

ANY time a spouse has an issue that is bothering him/her, it needs to be DISCUSSED. You need to talk to him. It seems like an innocent friendship to me personally, but if it is bothering you, than it is a problem, and you need to talk to him about it. Calmly, maturely and non attacking.

I would be inclined to text her myself. Thank her for her concern over your husband, but suggest she pay more attention to her own husband, and less to yours.

What's with this beating around the bush all about.

If he isn't up to anything, which I doubt, or he wouldn't be texting a married woman about his personal life, this married co-worker gets the hint. If he IS up to something, or what he's doing is going anywhere, that may just give both of them cause for stopping it.

I can tell you that without a doubt, I'd not be thinking about doing something, I would be doing something.