Yes, I had to address this very same thing with my wife, when she had her brief affair five years ago. I simply told her "I hope that isn't your boyfriend who you are texting from our own marital home -- that would be incredibly direspectful to me and the kids," and she mostly stopped doing it. The couple of times I caught her doing it again, I called her on it and reminded her that this was a firm boundary with me, and she did respect it and at least would take it outside.
The more important issue is one of CONTACT, however -- you are in a situation where your husband is still in contact with the OW, and you two supposedly have agreed on "no-contact," right? But he still does it? That's another matter.
In that case, I'd recommend saying "Look, we both know you are still in contact with her, and I already told you that I wasn't willing to live in an open marriage" (or whatever it was you did tell him about it when you agreed to no contact) . . . "so I guess we both have some decisions to make." And then end the conversation.
If he tries to lie about it -- or ANY time he lies to you and you know FOR CERTAIN (like you have proof) that he's lying, put your hand up in the "stop" position and say "Please just STOP IT. We both know you're lying to me right now, and it's incredibly disrespectful. As long as you're going to lie to my face about something so important, this conversation is over. I can't make you be faithful to our marriage, but I damned sure don't have to sit here and let you lie to my face, and I won't." (or something similar).
