Friend Got Cheated, Heartbroken Now

Your friend should make it very clear to her husband that this is not acceptable and is upsetting her.

I think this situation is very common, men AND women so talk to their exes and opposite gender friends emotionally and sentimentally, and such phrases that you mentioned (wish we married) maybe a splurge of the moment phrase.
Men and women do seek emotional support outside of marriage - and that is ok as long as it is not harming married life.

For me personally - it is not a big deal as long as it is only on chat and not consuming TOO MUCH of his time. But this is just me. My husband also talks to his ex-gf in similar ways you mentioned, and the girl also says stuff similar to what you mentioned like 'when you talk to my heart flutters' or 'butterflies in my stomach now that you are online' etc.

Involving parents would not be helpful as they may not be helpful in this matter - either because they won't understand or may think it is not such a big deal.

I would personally not give it too much importance and not worry too much about it - as it will fade away after a while. He MARRIED HER, the ex-gf is exactly that - an ex!!