Thin films of nearly symmetric diblock copolymers of poly(ethylenepropylene)-poly-(ethylethylene) (PEP-PEE) were investigated in confinement between two hard walls. The domain thickness was found to be a function of the film thickness. Mechanically stable films with an integral number of domains were found with the ordering parallel to the hard walls at all degrees of frustration. The PEE block was found to preferentially segregate to both the confining surfaces. A discontinuous first-order-like transition occurred in the number of domains. These results provide a new approach toward probing the influence of chain stretching (or dilation) on the stability of block copolymer structures.