As a first step in constructing initial data for dynamic black holes and general black-hole collisions, we study nonsingular vacuum Cauchy hypersurfaces with two isometric asymptotically flat ends connected by an Einstein-Rosen-type bridge. These hypersurfaces are assumed to be conformally flat and maximally embedded in spacetime but are neither spherically symmetric nor time symmetric. Three of the four constraints are solved explicitly for suitable extrinsic curvature tensors that possess linear momentum and/or intrinsic angular momentum. The complete initial data are shown to transform invariantly, modulo the sign of the extrinsic curvature tensor, under inversion through a minimal two-surface that represents the "throat" of the geometry. These and other properties show that the data represent a particular epoch in the history of a dynamic black hole. We describe the relation of our data to that of the Schwarzschild and Kerr balck holes. Finally, we discuss the generalization to encounters of two or more black holes.