You do need to talk to (a) your DH and (b) a solicitor about this really, MN is great for advice but people are not always totally clear about what they mean and it can be confusing so don't base any major life decisions. I also don't think there's a singular 'norm' as everyone's circumstances are different and you also need to distinguish between physical assets (usually the marital home but sometimes there are other properties such as a holiday home or investments to take into account, also cars, any valuable jewellery or antiques or similar), then there is cash assets like savings, stocks and shares and so on, then there are pension funds. How these things are treated can vary, you don't have to leave everything to one person or into a single trust so you might want to leave your house to your spouse but your cash and savings to the DC, for instance.
So for example, it's very common that spouses want the surviving partner to be able to live in the marital home for the rest of their lives/until they need to go into care but ultimately to pass on to their children, so you can create a property trust for the DC giving a life interest to the surviving spouse. "In trust for X with a life interest to Y" means X owns the thing but Y can use it for the rest of their life, so if it was a house Y can live there but can't sell it, when Y dies (or remarries or moves out of the house or whatever conditions you have put onto the trust) X gets to either live there or sell it and take the money. It's normal to nominate trustees who have a responsibility to look after X's interests and make sure Y doesn't try and sell up and pocket the cash or damage the asset. The trust can be for all the children in whatever shares you like, so DH could leave his half share in equal %s to all his DC including the SC and you could leave yours just to your DC, that's fairly common. So for example your DH has 2 children from his previous marriage, you have 1 and then you have one child together. Your DC has 3 children so he divides his 50% in 3 equal shares to them both, you have 2 and do 2 equal shares, so DH's 2 children with his ex get 17% of the house each, your child with your ex gets 25% and your child together gets 42%. This is usually the fair thing to do where the step children can also expect an inheritance from their other parent, if not it can feel a little unequal so you might want to consider equal shares, it's up to you.
To do this though you usually need to own the house as tenants in common, not joint beneficial tenants so you may need to investigate swapping the ownership around if you don't already. If you own it as joint beneficial tenants the ownership automatically passes in full to the surviving partner on the death of the other tenant, it's then theirs to do as they like with, you and DH could make mirror wills so whatever order you die in the house is left first to the surviving spouse then to the DC in whatever proportions you decide is fair but there's nothing stopping the survivor subsequently changing their will and they could in theory then choose to remarry and leave everything to their new spouse or cut the step children out or indeed leave it all to the donkey sanctuary so this involves a fair amount of trust/risk which the life interest system avoids.
Cash assets/ 'Money' is often treated differently, you can in theory also leave these in trust for the DC with a life interest to the spouse (or an interest until remarriage or whatever) but this usually means the spouse can't touch the capital, they can only spend the interest, so if you are relying on the money to live off in old age this may not work. And again it only works with separately owned assets, if it's in a joint bank account for instance everything will automatically go to the survivor. You can also leave other assets in trust, e.g. if your DH had some family jewellery he eventually wanted to pass to his DD but for you to be able to wear and use in your lifetime, this could be included in a trust so you wouldn't be able to flog it off - normally people trust one another over this kind of thing but I have seen it go wrong so anything particularly precious it is worth specifying in your will.