Yes, he should have helped. The only thing I could say in defence, is that perhaps it's become habit that all child-related matters are dealt with by you, so it didn't occur to him to think that maybe you might appreciate some help.
However, if he wants to remain in a happy married or have any kind of relationship with his DC, he needs to lose this attitude. If he carries on, you'll end up resenting him and his DC won't have any kind of meaningful relationship with him; he will just be a lodger in his own house as far as they're concerned. When it comes to DC, you get out what you put in.
You can't be a SAHM without your DH financing it. However, he would not be able to be the father of 3 DC and hold down his full-time job without you enabling him or him paying approximately £1500-2000 per month in childcare (assuming an 8-hour day) and an extra couple of hundred a month for all the housework tasks you perform. You both need each other equally. That means your relationship should be equal and that each of you should find life easier than if you were trying to do all these things by yourself.
It doesn't mean that you each do 50% of every single task, but that things balance out. As a rough idea, it should work out that you both have the same amount of child-free leisure time to do as you wish, without the other one constantly asking for direction on 'how do you...?' It should also mean that you have the mutual desire to support each other, whether that's listening to him after a hard day at work, or him coming home to poomageddon and saying, "here, I'll clean up downstairs while you take her upstairs for a bath."