Only in the very loosest sense could one say that if you are a happy Christian, then you are also a Buddhist, and vice versa. It is possible to be both, since Christianity is a revealed religion, and Buddhism is, at its source, a philosophy, not a religion. (When someone asked Gautama Buddha to discuss his view of gods, cosmology, etc., he declined to do so, saying that it did not have anything to do with what he was trying to teach: his philosophy.) Many people now identify as both Christians and Buddhists. They worship Christ and follow the Middle Way as well. But to say that Christianity and Buddhism are the same thing is, in my humble layperson's opinion, rather misleading and not correct.
You're right of course. However, think of the books it'll sell!
I hear what you're saying about being a Christian Buddhist. The former is a revealed religion, the latter a philosophy. However, I think there is a danger in trying to incorporate both, as it can obscure one's own Christianity, which is where the salvation is found.
How can a Christian be a Buddhist? Among other things, how can a Christian believe the universe does not exist?
To put it more simply; Christianity requires a belief, Buddhism is a way of living.