Emotional relationships lead to physical relationships. Kick him to the curb.
If I believe it, I would prove it. Then he would be moving out and the locks changed. With that said I am not one of those people who "believe" without some good reasoning. I do know some who are very insecure who think if there husband is 15 minutes late coming home that he must be seeing someone. That is their own insecurity talking.
Before anything else some factors are too important to consider such as:
-How's your relationship been going ? -Who is that woman ? -On what ground they meet ? And how's been your husband's behaviors in long term and if there been any huge changes in his behavior. Don't you have toxic relation history ?
Then, the first step is to make sure. Everything is just an accusation unless it proves otherwise, some accusations requires high prices to pay when you act upon them, i don't have to tell you this is one of them. You need to make sure you see right, you hear right and you getting the facts straightly on the point. Not always everything is the same as it seems.
People usually act so furious and mostly remove sense out of their mind. But you need to first balance your emotions and sense.
Generally, this is so inappropriate, if the relationship be strong and unite enough, there wouldn't be no leak. So if he falling for another woman, means his feelings might not be as stable as it should be over you.
This is where the possibilities, thoughts and wonders start to form.
It's possible that your husband is betraying you which if it be as straight as it sounds then you need to kick him out of your life, cause you deserve better and you need someone to be able to trust.
But the point is maybe the problem is not your husband, maybe that woman knows some weak spots of your husband and she trying to take advantage of him and that creates the atmosphere of your feeling through his emotional connection over the woman.
Maybe they are just too much up to what they do and you're overthinking the matter while nothing really is going on but the business that they're up to.
And you need to think about it a bit deeper and involve yourself, even if the fact be that your husband really falling for another woman and you had a very good relation so far, then you need to ask yourself, "What is that emptiness that your husband is feeling which lead him to seek it into someone else's arms" ? Then try and do your best to fill that. Once you do that, you'll get back your husband.
So the best way of realizing all of this, is communication. That's what i would do.
Are you, aren't you anyway responsible for his emotional refuge?