The only problem that I can really see is mixing religions, and the biggest part is marriage and children. It is very possible to teach children of more than one religion, although as they get older, if there are extreme differences they will probably want to stick with one, which could be upsetting if one partner would prefer their child follows them.
For any ceremony such as marriage, it is difficult, although not impossible to combine the two cultures. I would more expect that one culture would just take over though.
To make a mixed-culture relationship work, you need to be open and willing to compromise on many things. I think that culture is a wonderful thing though, and it is much more interesting when different people are combined than seculded.