It is a little of having cake and eating it too. But is there something wrong with that? How many people want to have cake but never eat it?
But there is a deeper answer. Love is not limited. If you love someone new, that does not decrease your love for anyone else. What is limited is the time people can spend together.
One way to imagine this is to think about a parent having a new child. They don't love their first child any less. What is important is making sure tha the first child still feels love and time is still spent with him or her.
So one way to deal with this is to realize that his feelings for her are independent of his feelings for you. While he is out with this woman then that is a good time for you to do something fun for yourself. Go out with friends or pamper yourself at the spa or watch some favorite movies. Have a night out with some friends or go on a date yourself with someone else. Keep yourself occupied so you don't dwell on it.
The most important thing is to communicate what you are feeling. If you feel jealous, it iss ok to say so. That doesn't mean he has to fix it. The best way to deal with jealousy from what I have seen is to find the root cause of it like envy or insecurity and deal with that.
I wish you well.