Instead of forming a typical bilayer or monolayer membrane, both the bridge (I-shape) and loop (U-shape) conformations coexist in the planar membranes formed by ABA triblock copolymers in a selective solvent. The non-equilibrium and equilibrium relaxation dynamics of polymer conformations are monitored. The non-equilibrium relaxation time depends on the initial composition and increases with an increase in the immiscibility between A and B blocks. The equilibrium composition of the loop-shape polymer is independent of the initial composition and A-B immiscibility. However, the extent of equilibrium composition fluctuations subsides as the A and B blocks become highly incompatible. The influences of the A-B immiscibility on the geometrical, mechanical, and transport properties of the membrane have also been investigated. As the immiscibility increases, the overall membrane thickness and the B block layer thickness (h) increase because of the increment in the molecular packing density. As a result, both the stretching (KA) and bending (KB) moduli grow significantly with the increasing A-B immiscibility. Consistent with the case of typical membranes, the ratio KB/KAh2 = 2 × 10-3 is a constant. Although the lateral diffusivity of polymers is insensitive to immiscibility, the membrane permeability decreases substantially as the A-B immiscibility is increased.