The rigidity of collections of points and the rigidity of collections of circles in the extended complex plane is proven by Beardon and Minda using a maximal amount of conformal invariant information. Crane and Short generalize this work to collections of points and collections of spheres in higher dimensions. Both use a notion of the cross-ratio for 4-tuples of points, while for circles and spheres, the inversive distance between pairs is used. When a collection involves intermingled points and spheres, these conformal invariants can no longer be used. Working in Lorentz space, as Crane and Short do, we develop a notion of an invariant known as the Lorentz ratio, used as a conformal invariant between a point and two spheres. The Lorentz setting allows for an understanding of the correspondences between several geometries, and here, the rigidity of intermingled points and spheres of R ̂^n can be seen as part of the more general statement of the rigidity of intermingled points, ideal points, and hyperplanes of hyperbolic (n+1)-space. This rigidity statement is accomplished via the new conformal invariant.