Novel lamellar mesophases which are quite distinct from conventional smectic mesophases were obtained with a bolaamphiphilic triblock molecule composed of a rigid biphenyl core, two polar 2,3-dihydroxypropoxy groups in the terminal 4- and 4'-positions, and a semiperfluorinated chain [O(CH2)6C10F21] in the lateral 3-position. The competitive combination of microsegregation and rigidity in this molecule leads to layer structures in which the bolaamphiphilic cores segregate from the lateral chains into distinct sublayers. In these sublayers the biphenyl cores are aligned parallel to the layer planes. Decreasing the temperature leads to a subsequent inset of orientational and positional order of the biphenyl unit, which leads to a transition from an uniaxial SmA phase to a biaxial SmAb phase and finally to a mesophase with an additional periodicity within the aromatic sublayers. Here, microsegregation occurs on two distinct levels: The segregation of the nonpolar chains from the aromatic cores leads to the "bulk" layer structure and segregation of polar and aromatic subunits within the aromatic sublayers gives rise to an additional periodicity within the aromatic sublayers. These phases can be regarded as smectic phases built up by quasi-2D layers with nematic, respectively SmA-like order, separated by isotropic layers of the lateral chains.