I talk from similar experience .
My situation is slightly different as he refused to admit it , telling me he was so happy he loved me etc . Eventually I stopped demanding to know where he was , as his nights away from home steadily increased . It was futile to accuse him as he would never ever admit it and I could never actually prove it. I just knew. It got to the stage he was "working away" up to 3 or 4 nights a week.
When he was home he acted like a real family man and projecting an image to all and sundry of what a great guy he was . I lived a lie for 6 years. He thought he had it made, a wife at home to look after the family, and a bit on the side for six years . The most soul destroying 6 years for me.
Your DH wants to have his cake and eat it too, plain and simple. How dare he treat you like this . Trust me he knows how this hurts you, yet he does not care about you enough to stop.
Do not do what I did . Please leave this man now. The best thing I did was tell one person , I too thought I had no one but all it took was telling one person . i will never forget the stunned reaction this one person had, and yet for six years I had normalised everything.
You deserve so much better than this ,you really do.
I will never forget the countless nights sitting alone at night, the children in bed, feeling utterly alone and bereft as I knew He was with someone else . It makes me so sad to think of you potentially doing the same . It's no life , living a lie. No life for you or your children.
Please tell somebody , and take it from there. I knew when I told one person , just one person close to me I could not go back. I don't deny it was hard , very very hard to get the words out. But when I did ....my god that was it .
Apologies for the long post . I just want to tell you from experience how you cannot live like this , it will destroy you .
I am happy now, very happy with a man that truly loves me and demonstrates that with respect and care and love every day for me and my DC. You deserve a better life too, you really really do .