My 16-year-old step-daughter is similarly glued to her phone. Before we cut her off for not paying the bill, she was logging **6000** text messages a month (for those who don't want to do the math, that's 200 per day).
But she has the excuse of being a teenage girl, and we expect nothing less
I don't have any specific advice, but I agree with you and everyone here that his manners are lacking. It's great to be in love and to express it, but you deserve attention too.
It doesn't do any good to impose superficial rules his texting behaviour. Artificial constraints treat symptoms, not underlying issues.
He's probably just being an oblivious guy and doesn't realize how rude it is. Guys tell me all the time that they really are oblivious, they don't do these stupid things intentionally to piss us off, they're just genuinely clueless.
Maybe if they had more face-time, they wouldn't feel the need to text so much?
At any rate, if she's cheating on her husband, it's only a matter of time before he finds out and the whole thing explodes in their faces. That should put a quick and sure end to your problem...