I was in a similar situation last year Daisy, and I can really sympathise. I noticed that my dh had exchanged texts with another woman, ending in xxx. Content was fairly innocuous - 'how was the conference', that type of thing. BUT.. he rarely mentioned this woman and I certainly didn't know he had any contact with her other than an occasional lift as part of a group of friends. There were also pretty regular phone calls - maybe 4 or 5 times a week, not several times a day. I was gripped by fear that this was an affair, or leading to an affair - even though I'd have no reason to suspect my dh otherwise.
I won't go into all the details, but by keeping tabs I realised that he was systematically deleting her messages/call register and had deleted an email he'd sent to her from his PC. Again, the content of the email was very bland.
Unfortunately I didn't know about MN then, so this is what I did. I built up some 'evidence', and kept a note of anything I found, her phone number, etc. I then spent about 3 weeks plucking up the courage to speak to him. I knew I'd have to admit that I'd looked at his phone, so I needed to make sure we weren't going to come out of this with me looking like I was in the wrong. When I finally did talk to him, I presented it as 'I'm upset and jealous about what I saw on your phone - can you tell me about your relationship with this woman'. I also didn't tell him everything I knew, so he almost immediately lied to me, which caught him out.
He never admitted this was a flirtation (although I think it was), was totally reassuring about our relationship and his feelings for me, and admitted that he shouldn't have lied about it. He admitted his actions looked suspicious, and would be jealous as hell if it was me! He was going through a very hard time at work, felt isolated and just enjoyed having 'a friend' to chat to. He immediately agreed to cut off all contact, or to allow me to meet the woman. I chose the cutting contact option, obviously!
If I was reading this from someone else I'd be sceptical, but I am convinced that he did not consider this flirting. Although if it was 100% innocent I'm not sure he'd have been so quick to agree to cut contact. Either way, I caught it before it developed into anything. I think he was enjoying a bit of mild flirtation, but as soon as I knew about it he suddenly saw what he was risking and decided it wasn't worth it.
In hindsight, I wish I had spoken to him sooner, to save a bit of heartache. At times, I wished I'd never found out, but now I'm glad I did as it also started us talking about how to improve our relationship.
Anyway, don't mean to hijack your thread but I thought you might like to hear that these things can turn out OK. What your husband is doing IS suspicious and unacceptable to you (as mine was). BUT, it could still be poor judgement, mild stupidity and getting a bit carried away, rather than infidelity.
I'd say nip it in the bud.