We have studied a binary mixture of compounds, one of which has rod-like molecules and the other bent-core molecules. The rod-like molecules are biphilic in nature with a long alkoxy chain attached to an aromatic moeity only at one end, and exhibit the bilayer SmA(2), phase, even though they do not have the highly polar cyano or nitro groups. The compound with bent-core molecules exhibit the B-2 phase which has polarized layers with tilted molecules. Three liquid crystalline phases are induced in the binary mixtures, depending on the concentration: the 2-dimensionally ordered B-1 phase for compositions with 15 to 63 mol % of the rod-like molecules and the B-6 phase for 63 to 87 mol %. The sequence obtained on increasing the concentration of rod-like molecules is the same as that seen on shortening the chain length of the BC molecules. Between 87 to 95.5 mol % of the rod-like molecules, a new biaxial smectic A(2) (SmA(2b)) phase is induced. On the basis of several observations, we argue that it corresponds to a structure in which the BC molecules are reoriented with their arrow directions pointed along the layer normal. The SmA(2) to SmA(2b) transition corresponds to an orientational transition of the bent-core molecules in the anisotropic SmA(2) background medium.