The out in public with kids and metamours is something that has to be negotiated and the well being of the kids taken into account. Is he married? If so, what will his wife be comfortable with. I have a 15 year relationship in which there are two kids and they are only to think he and I are friends. That is their parenting decision. I am not happy about it, but not unhappy enough to terminate the relationship. Though I must admit that it is not my main priority right now.
Now, the person that I had pizza delivered with also has kids about the same age as my 15 year relationship. His wife wanted me to stick around and talk so I ended up meeting the kids. I was amused to hear " Oh red hair, how pretty! Way to go Dad!".
We have a child that is my husband's by his first marriage. She is not allowed to even meet our other partners because it could cost us custody and visitation rights and that is not a risk my husband is willing to take. Definitely different parenting styles.
How do you want to handle things with your own children? How does the new boyfriend want or need to handle things with his kids?