There are infinite number of scenarios that mark cross cultural marriages in relation to in laws that it seems a daunting task to pull any overarching themes together. You could have parents who supported your marriage, those who grew to support it, those who opposed, those whom you live down the block from, under the same roof, across the world, divorced parents, dysfunctional parents, etc. But I'm going to try. And I'm going to use my old friend Alliteration to help me.
R-edefine your idea of family. This is poignant between American and Chinese marriages like us. Simply because the definition of family differs so drastically between the two cultures. Generally, Chinese culture places stronger emphasis on the joining of two entire families when two single individuals choose to marry. What sort of model your marriage will adopt is something the couple will have to work out together. I know my American friend chose to live with her Chinese mother in law after they had their first child. J and I most likely will never find ourselves in that situation, ahem, by choice. Whatever ends up being characteristic of your marriage in your relationship with your spouse's family, it's not a bad idea to begin by recognizing some of your assumptions of what that picture might look like is not universal, and to be open-minded and humble enough to stretch the definition of family to accommodate your new family of another culture. This will not be a comfortable process, but again, the reward is there. All cultures supply solutions to society's problems differently, and you will be enlightened by some of those solutions which you never considered within your own culture. (Of course you will discover problems you never knew but let's stay positive, shall we?)
R-emember your families didn't choose to marry you into another culture (unless they did so through arranged marriages which would be subject for an entirely different sort of blog post as this particular one), so you can't expect them to make the effort to reach cross culturally as you did. It takes a lot of work to engage another culture. Your parents have their own lives, and yes ideally they would be the type of people who make that effort, but if they're not, you can't really blame them. J and I try, not very hard to be frank, to explain to our own parents why our spouse acts the way they do, and meet with blank stares. Both our parents have grown up in a very monocultural world without too much meaningful encounter of other cultures, it is sometimes too far of a stretch to get them to see from our perspective. And it is unfair because they don't live in close proximity with someone of another culture daily as we do. Perhaps lowering expectations in this area will improve life with in laws in a cross cultural context.
R-espect your parents/in laws. It's common courtesy, it's civil, it's Christian, it's filial piety, whatever you call it, just do it. Perhaps it's the Chinese part of me, but as a parent myself, I know firsthand the kind of unconditional love you have for your children, and it's important to respond in respect. And I believe doing so goes a long way in displaying respect for your spouse. The problem with being in a cross cultural marriage is respect is shown differently in each culture. My advice is to take cues from the local, ie., your spouse. For example: Chinese people generally only make a big deal of birthdays when you are a young kid, but I've learned acknowledging birthdays is a very meaningful event in my American family and try to adapt to that custom.
And by popular demand (okay 2 people suggested it), raising children up next.