I've had two relationships since my hubby (one still around ) and to be honest discipline is left to me for my kids. Occasionally I'll get a 'look' if he thinks I'm being too harsh (or soft !) and we'll discuss it later but he never steps in. It works better for us like that as it maintains a good relationship between him and the children, and it means neither of us undermines the other.
I guess the answer is communication, making sure you both discuss it carefully and know where you both stand ?