| | Re: is this an emotional affair?
Your husband shouldn't be doing this--the fact that it bothers you this much should be reason enough for him to stop. But that said, it may be too soon to give him an ultimatum. As long as your husband hasn't told you that you can't come along, you might try going with him every time he goes walking with the Other Woman. It would be good for your health too, anyway, and if you have trouble keeping up at first, they should be able to figure out some way to accommodate you. (For example, if they're starting out from a parked car, they could take two short loops instead of one long one, and you could sit out the second one. And be sure to give your husband a big public display of affection when he gets back.)
It's inappropriate for these two to be alone together like this, but if your husband wants to continue the walks, you should always be involved in one way or another, to chaperone, or mark your territory, or whatever. And it would show your husband (and the Other Woman) that you care enough to protect your marriage. Words obviously haven't been working, but getting up at 5:30 a.m. and trying to walk five miles just might.