Do you have a similar set up in terms of ages, as the op?
I think it is very easy, with very young children, to see them as “one of your own”. Especially if there are no older siblings their side.
It is difficult and probably undesirable to do so, if the children are older. I was 10 when my step parent because a part of my life, they had no children. They were encouraged by my parent to dive headlong into “parenting”. This wasn’t the right approach it turned out, for me. It made me awkward and belligerent. They stepped back and let the relationship build naturally. Almost 25 years later, I love that step parent just as much as my biological parents, this has been the case for around 15 years. They are my child’s favourite grandparent.
I have 3 step children and my own child. I interact differently with all 4 children, there is little I do the same across all of them except being very consistent around basic manners. They are all so, so different. My dh struggled with that initially, he has no experience of being a stepchild whereas I do. We talk all the time about the families relationships with each other, pressure points etc.
It’s not black and white with blended families op -open communication is key. Don’t let things fester, don’t let it become an argument, you and your partner are a team here but what’s right for you might not be right for him, right now.