Finding it mildly amusing that someone calling themselves RejectofAllah is playing devil's advocate...
I lived with a controlling bastard for 10 years was told practically when I could breathe in and out. My friendships were discouraged and the previously civil relationship I had with my ExH was banned completely. Without reason to be honest, but that is the nature of a seriously f*cked up individual.
Would I allow anyone to tell me who I can and can not be friends with? NO.
HOWEVER....
The conversations you quote toplist are not the hello, how are ya? lovely weather we're having type conversations are they, they are a lot less innocent and I totally understand how you are pissed off by them. IMHO, rightfully so.
His emails to her are a betrayal of you, this blah blah about where his life went wrong is just disgusting! How the bloody hell is that supposed to make you feel, hearing that? How would HE like it?
Your comment about her being upset when you got engaged is enough for me to state categorically that clearly, regardless of her current relationship status, she is NOT a friend of your marriage, and your H is lapping up all the sneaky, underhanded attention she is lavishing on him.
She can't be happy and fulfilled in her relationship either, or she'd not be stirring the shit in yours. He has said as much, so I would sit him down and calmly explain that while you are fine with him having contact with who ever he likes, that to discuss you, your family and complain about your life to an Ex who is clearly biased against you is what you consider to be betrayal.
State that electronic to-ing and fro-ing between them in it's current form is verging on an emotional affair, and it needs checking and it needs paring right back. You are not saying they can't speak, but he needs to really be consious of what is being said and what the effects of this will be.
This guy needs to realise that if this kind of conversation were being had in a public place in front of both her partner and you, there would be a scene.
The flight over italy reference .... this is not a Mile High Club thing is it?