Science and religion do Not have to conflict with one another.
Science uses "applied common sense" (observation and logic) to explain the What and How of the universe. Technically speaking, whether a (transempirical) God exists or not is simply not (empirical) Science's concern. Religion, on the other hand, relies on "faith" to grasp the Why of the universe, the "Meaning of Life," which many associate with "God."
Problems arise when one tries to do the other's job.
Can Science and Religion work together to give a broader picture of reality than either alone? Depends what you mean by Science and Religion.
Science: is it defined by Method or by nature of proof? If by nature of proof--meaning strictly empirical--then No, they can't work together. But then, you're really dealing with Scientism and the problems inherent with a strictly empirical POV. If you define Science by Method--and that the tools used and data collected should reflect the domain being studied--then I would say, at the very least, that the potential exists for Science and Religion to complement one another...provided that Religion means a mindset that is open to Truth and not cemented shut by ego-serving dogma.
"Science without religion is lame, religion without science is blind."
Albert Einstein, "Science, Philosophy and Religion: a Symposium", 1941