Binary mixtures of two alkenyl side chain bicyclohexane compounds have been prepared, one a pure nematic phase (1d(3)CCO2) and the other a pure smectic B phase (0d(4)CCO2). These two compounds are characterized by similar molecular structure, except for a shift in the position of the double bond. An interesting observation in the phase diagram is the occurrence of a two-phase (smectic B-nematic) co-existing region (approximate to 2.5-3 degrees C) for a small concentration range (x = 0.55-0.8) for these mixtures. Density and refractive indices (n(o), n(e)) have been measured for these mixtures. In the co-existing smectic B-nematic phase, we have been able to measure simultaneously the refractive indices of both the smectic B and the nematic phases. The refractive index and density values have been analyzed to yield orientational order parameters. From the Differential Scanning Calorimetry (DSC), density, and birefringence measurements, the nature of the smectic B-nematic phase transition for these mixtures has been assessed. The behavior of this phase transition with concentration is also reported.