Blended Families. Differences in parenting.

We both have kids from previous marriages. My two sons are 9 and 12. His son is almost 16. We’ve been together since they were 3, 6 and 12. Our biggest struggle is a fairly big difference in parenting styles. My sons are with us 50% of the time. His is here 100% of the time. We have tried, for years to mesh the way we parent and it doesn’t work. I’m an emotional support teacher. I feel like I run a pretty tight ship with my kids in regards to chores/expectations. Adam was raised by his dad who was always working. His son’s mom lives 1600 miles away and does little to nothing to help raise her child. Adam, in my opinion, is a very permissive parent. In his eyes, his child is perfect. If it is ever evident that his child is in the wrong there is always an excuse or reason for it. Two years ago, after many fights and almost break ups, we pretty much stopped dealing with each other’s children when it comes to parenting...which sounds awful, I know. We completely love each other...we just were raised differently and have completely different ideas on raising children. Our styles are never going to mesh. I’m not willing to be as permissive with my children because the world will not be and he’s not willing to hold his child to the standards that I hold mine. I have explained to my kids, because, let’s face it, this probably seems super unfair to them, that I raise them the way I do because I feel it’s best in order to make them independent and well-functioning adults. Adam raises his son as he does because he feels it is best. My kids are cool with it. In 2 years, his son will be an adult and this will be a nonissue. Does anyone else have something that just doesn’t quite work with a blended family? How do you deal with it? Completely avoiding the issue is not my preferred coping method, but it seems to be the only one that works for us in this topic.