R.K.
I agree with many of the women who responded in that your husbands ethics should be questioned in this situation. If you want to go behind his back and tell her somehow, set up a fake email address and anonymously tip her off. I don't recommend going behind his back, but if he already told you he wanted you to keep this a secret, then I don't see why he would change his mind on this. If you tell Jane that it is you, it WILL come back on you - I guarantee it. It's ultimately up to you what you do, but your husband shouldn't be friends with a guy who would do that to his wife.