I'm not even going to pretend like I have any decent advice to give concerning raising children in a cross cultural marriage. I have two kids, at the time of writing, seven and four. There is a long way to go before anyone can make judgments of our parenting skills. So without offering any solutions to people seeking advice on how to raise bi (tri, multi) cultural kids let me offer you the challenges of cross cultural parenting. (I know, you're welcome.)
If culture shock is an issue for you before your pregnancy, having a baby is going to kick it into high gear. Because, with that final contraction and push, you've birthed an entity outside of yourself which has your entire heart wrapped around it, your culture bound expectations of life attached to her, and an innate instinct to protect and defend him no matter the cost. This is a precarious position to be in while encountering culture shock because you're confronting something that is attacking not just your cultural values, but also attacking the little being through whom you naturally want to preserve the values you hold to be true. Many times, this very dilemma has kept us from embracing Chinese culture while we lived in China, because we simply didn't have the courage to subject our children to the cultural differences they will inevitably confront. For example, we decided to pull our daughter out of the Chinese preschool system because we sensed the teachers using tactics like shame, which is very sensible within Chinese culture, to teach our very free-spirited daughter. For more on my experiences with my kids in Chinese school system, see here and here.
Every cross cultural couple, or expats, who think about having children anticipate raising their children bilingual. No one can deny the benefits of the gift of bilingualism. But it is never as easy as you imagine, and although I have seen, or heard about, people doing it successfully, they are few and far between. The best advice I can give to people is to set realistic expectations. For me, it means grappling with the reality that my kids are never going to be as bilingually fluent as I am. My bilingual abilities are a product of my environment which my kids do not have. Of course, being bilingual may mean different things to people. I am bilingual in that I can speak and understand both languages and be comfortable developing meaningful relationships with people of both Chinese and American culture. For some, being bilingual may mean being able to read, speak, write, and get PHD's in both tongues, for others it's being able to simply speak "market language". The best outcome I have seen of people raising bilingual children are instances where the mother and the father have a different dominant language. Jason and I both have dominant languages in English so it was an uphill battle to raise our kids in Chinese. If you are committed to raising bilingual children, there are certainly some quality resources out there to help you.
Language is only one aspect, though certainly a significant aspect, of culture. I grew up with lots of missionary children and some of them can speak Chinese fluently but very few of them embodied Chinese culture. And that's because their Western families were the primary influence in the formation of their worldview. With parents coming from two cultures, the challenge is to decide, hopefully together, what worldview and values to pass on to your child. Note some of these will be conscious decisions that you and your spouse discuss, but I think many of these are simply passed on subconsciously because of our unquestioned assumptions. These decisions range from material things such as food, clothing, routine (no sensible Chinese family puts their child to sleep anytime before 9:00), to the way you treat your parents, people in your community, etc. Sometimes I see the way my children behave and am astounded by how American they are. Those are the moments of disconnect for a Chinese Mom raising children with an American husband. Just the other day I was in tears to J, grieving that some of my favorite things to do (okay eat, I'm Chinese!!) when I was a little girl are not things my kids love. But I know we are giving them countless invaluable experiences by exposing them to the best and worst of both cultures. I also know, from deep personal experience, that it is not the easiest life journey. My prayers are they will learn at a young age, sometimes being uncomfortable is the path to treasured blessings.