Greenhouse was born in San Diego to a British mother and a Canadian father who was Stateside to finish a Ph.D. in geophysics.
Her family moved back to Canada when she was four years old; Greenhouse, who has four brothers, was a student at Queens studying psychology and dabbling in theatre when she decided she wanted to do both. A double degree was the answer. Still not sure one could have a career as an actor, she gave herself two years to get it going or move on. She found work immediately.