Marriage and relationships

It would depend on other things too.

Are you happy?
Not necessarily in your marriage situation, but do you find satisfaction in life?

If you divorced and had the kids, would be support them, and would you be able to go back to work? What would your finances look like before and after the kids turn 18?

What kind of drugs?
Are they drugs that will cause him to sooner or later lose his job, and there goes the financial stability, including perhaps the loss of your home?

How old are you? How old are the children?

Would you want to look for another relationship, and if so, what are the prospects? Do you need to have a relationship to value yourself?

What would your life look like if he wasn't in it? Would you be happier and better off?

Divorce is a young persons game, IMO.

Different peoples tolerances vary, and you must decide for yourself, and in this case the welfare of your children, what you can tolerate and still maintain happiness/life satisfaction.

Don't ask other people what they would do. They don't live in your skin.

I don't call that a marriage. I would leave and make my own happiness.

They say bad marriages are kept together by money, sex, or the kids.

Sounds like you have at least two reasons. ( you don’t mention how he is in bed with you)

If I were financially stable because of my mate's job, and they had a drug problem and likes to sleep with other people - basically couldn't care less about me, and our children, I would talk to my make about about his responsibility being more than about financial support, but being an example for his children, and being faithful to his mate.
If he does not listen, and change, for the love of my children, and not wanting them to grow up thinking their dad's behavior is normal, and a submissive wife is to be disrespected, or whatever crazy ideas they may have as they grow up, the next time my husband heard me would be when he gets the divorce papers, since I would be making sure he didn't bring home something that would be worst - like HIV/AIDS.
That's me... but let's talk about you.

I'm sorry you are going through that.
The question is, are you living with it because you think you deserve it, because you are no good, worthless, and can't make better of yourself?

If you feel this way, please be assured that no matter what a person has done in life that makes them feel unworthy, they can pick themselves up... because you are somebody. You have worth. You are loved.
So don't let anyone - anyone - treat you like you are worthless.
You can make better for yourself, and show your children how to be strong, because they too will face challenges like you.
If you are not there for them, they will be left on their own.
I think it's in the power of your hand, to teach your children.

That said, I don't know you. I don't know what your background is. The only thing I know is that people can do better, if they want to.
I hope you do.
Regards.