Creating emotional intimacy with someone other than your spouse is cheating, at least in my book. I would be upset as well. My wife had an affair and it started the same way as with what your husband is doing.

It was friendly at first, they had been attracted to each other but never dated, he was in an unhappy relationship and before you knew it they were having an affair.

I would express your concerns to him. If he cares about you he will take into consideration what you say and cut ties with this woman. If he doesnt I might be worried. Good luck.