Well the Bible says not to marry a non Christian, and also that a man should lead his wife spiritually, and that a woman should follow her husbands lead. I do not know much about the Wiccan beliefs but I think that a Christian man would have difficulty leading a wife with different beliefs, and would be going against the Biblical teachings. A Christian woman would not be able to follow her Wiccan husbands lead as she would disagree with his worldview. So right off the bat the Christian in the relationship would be compromising their beliefs. As I said I do not know much beyond the superficial when it comes to Wicca so I am not going to break down how the Wiccan partner would be compromising their beliefs, but I am sure it would be an issue at some point. Another issue would be whether or not to participate in one anothers religious events, or practices. How talking about spiritual issues would work, how to seek advice when the source of morals, and meaning are derived in very different places.
I think the couple could find a way to be "happy" together, but not without some serious cognitive dissonance, and likely some unhealthy resentments and dissatisfaction.