We analyse recent ESR measurements on Ca2+ ATPase and Myelin proteolipid apoprotein reconstituted in phosphatidylcholine bilayer membranes. Our intention is to discover whether the measurements indicate significant protein-protein repulsive or attractive interactions. In order to do so we have studied a model of a lipid bilayer membrane containing transbilayer proteins. It represents the proteins by hexagons moving on a triangular lattice interacting via an energy E0 which can be attractive, repulsive or zero. The last-named represents that all of the Ca2+ ATPase data is best described either by the "random" model or, possibly, by one in which there is a small repulsive interaction, but not by the "annulus" model or one in which there is always at least one layer of lipid chains between every pair of proteins. We find that all of the Myelin PLA data is best described by a "random" distribution of hexamers and not by an "annulus" model of hexamers. We suggest measurements that can be done in order to unambiguously settle the question of whether these systems are best described by a "random"-type model or an "annulus"-type model.