A common feature of the recent calls for reform of the undergraduate biology curriculum has been for better coordination between biology and the courses from the allied disciplines of mathematics, chemistry, and physics. Physics has lagged behind math and chemistry in creating new, biologically oriented curricula, although much activity is now taking place, and significant progress is being made. In this essay, we consider a case study: a multiyear conversation between a physicist interested in adapting his physics course for biologists (E.F.R.) and a biologist interested in including more physics in his biology course (T.J.C.). These extended discussions have led us both to a deeper understanding of each other's discipline and to significant changes in the way we each think about and present our classes. We discuss two examples in detail: the creation of a physics problem on fluid flow for a biology class and the creation of a biologically authentic physics problem on scaling and dimensional analysis. In each case, we see differences in how the two disciplines frame and see value in the tasks. We conclude with some generalizations about how biology and physics look at the world differently that help us navigate the minefield of counterproductive stereotypical responses.