This topic is certainly nothing new and it seems like it is getting more and more common. You have 2 split families, each with their own children and two adults trying to make it work.
In many cases like this, there is shared placement with the other parents, so you and your partner will have some kids sometimes and other kids other times, which can make for problems when planning activities and such.
So, are there any tips or good advice for these families, well, of course! A family calendar could be helpful, giving everyone a central point to write in activities, family gatherings, etc. The calendar could be coded in a way where it would be easy to see when and which kids are there and not, possibly just by labeling initials in different colors or something similar.
I have heard many parents complain about how the others' child or children doesn't listen, or misbehaves when their mom (or dad) is not there. We are all familiar with the "wicked stepmother" analogy too, which can also play a part. It is human nature for people to treat their own children differently than someone elses. I believe that the key in making things work is trying, to the best of your ability, to be fair. Do not show favoritism, it will only make matters problematic for all involved.
When a child misbehaves and needs to be punished, BOTH parents/adults need to agree and support each other. Always follow through with punishments and rewards. It works both ways, the kids deserve to be rewarded also and they are desperate for approval and recognition. Show the kids that you love them and give them your time and attention as much as you can.
Another very common-sense approach to keeping the peace and having a happy home, is to treat each other with as much respect as possible. The children watch the interaction of the adults and if Mom is talking down to Stepdad, the child will think it's okay to do that, and vice versa.
Parents/adults also need to make sure to share some private time together, without the children. It may be helpful to set a certain day of the week to have a discussion or chat session about any concerns or problems that are going on. Be open with each other and be courteous.