Leaving your husband because your feelings hurt or you believe something is going on isn’t the best move. You need more than a hunch. My advice would be either get some proof or leave it alone. Harping on it will only make it worse.
I’ve had a few very close relationships with married men I’ve worked, one inparticular. We are great friends, but mostly during business hours, we rarely talk on weekends or after work, but i would have to say his is one of my best friends and his or mine marriage statics has nothing to do with it. Nothing more than friendship. I’m not saying that you don’t have reason to be upset but if you trust him… trust him. Otherwise you have more problems than a friendship at work.
When another person intrudes in your marriage and takes time and affection and trust away from the marriage then that’s a sign that there’s an inappropriate relationship with that person. When that person is causing tension and uneasiness in the marriage that’s another huge red flag.
Your feelings are justified. They may not be cheating but it doesn’t sound as if this is a healthy friendship with this woman. The giddiness and closeness and emotional intimacy he shares with her is one that ought to be shared with you and I get the impression that you’re not feeling those things with him. He’s definitely crossing some boundaries with her and he’s choosing not to recognize it right now.
The fact that this relationship upsets you is enough reason for him to pull back on the friendship and delegate it to a professional-only relationship. Preferably, the only contact they should ever have is passing in a hallway at work. If he has the option of never working with her then he needs to take it. He should not ever be talking to her about anything personal especially nothing to do with your marriage or your family, nor her marriage or family. If he sees her in public, a wave hello and nothing more.
Hopefully he’ll realize how damaging this relationship is and he’ll take his marriage seriously, putting his marriage above this friendship that appears like a schoolboy crush.
Is there any way you can talk to this woman’s husband? I’d try that first and see what he feels and thinks about this “friendship”, then if he’s as miffed as you are I’d talk to your husband again and lay it down. Such as “this relationship is inappropriate and if you can’t end it then I will be leaving” I’d have to say I wouldn’t be willing to give a inch at all just based on his “excitement” when he sees her. Screw that. If it means he needs to try to find a new job to save your marriage then that’s what it means.. and if he’s not willing to do anything then there’s your answer right there.
Does not sound good. Kissing her on the cheek really! You have to have a good talk with him. It looks like he really likes this women. 
Nail her hubby.
Like my mother use to say Keep your friends close and your enemy’s even closer. Invite the couple over for dinner, What do you think he would do if you paid more attention to her husband? Would he be jealous or not?
While it’s possible for him to have a female work friend (my husband has had those), in two years, they should not be so close that she is “close to his heart.” Work friends who don’t see each other socially really aren’t so close. However, if you interrupted this woman while she was on a phone call, I can’t agree that she was rude. While you may be blowing things out of proportion, if another woman is causing these problems in a marriage and making you not trust your husband and think of leaving him, this should be a signal to him that if he wants this marriage, he needs to ditch the friend because his commitment is to you. However, if he thinks that you are jealous and possessive, he may decide that this marriage is not for him. Good luck