Science and faith are compatible in the sense that both are used to define and comprehend life. Many great scientists of the past were committed Christians such as: Nicholas Copernicus, Isaac Newton, Blaise Pascal, Robert Boyle, Michael Faraday, and James Clerk Maxwell. Copernicus even said: "It is my loving duty to seek the truth in all things, in so far as God has granted that to human reason."
Contemporary scientists who are also Christians include: John Lennox (mathematics), Willam Dembski (mathematics), Michael Behe (biochemist), Hugh Ross (astrophysicist), and James Tour (chemist and nanotechnologist). These scientists and many more demonstrate that faith in the God of the Christian Bible is reasonable as well as remarkable, and is based on objective, historical, and archaeological evidence.
This is my favorite quote by Professor John Lennox: "Faith is not a leap in the dark; it’s the exact opposite. It’s a commitment based on evidence… It is irrational to reduce all faith to blind faith and then subject it to ridicule. That provides a very anti-intellectual and convenient way of avoiding intelligent discussion."
To me, believing in a supernatural dimension is not like believing in magic or fairy-tales, it's more like believing in something greater than myself that contains concepts such as: beauty, friendship, romantic love, courage, justice, and goodwill.