  The striped phase exhibited by a spin-$1/2$ Bose-Einstein condensate with
spin-orbit coupling is characterized by the spontaneous breaking of two
continuous symmetries: gauge and translational symmetry. This is a peculiar
feature of supersolids and is the consequence of interaction effects. We
propose an approach to produce striped configurations with high-contrast
fringes, making their experimental detection in atomic gases a realistic
perspective. Our approach, whose efficiency is directly confirmed by
three-dimensional Gross-Pitaevskii simulations, is based on the space
separation of the two spin components into a two-dimensional bilayer
configuration, causing the reduction of the effective interspecies interaction
and the increase of the stability of the striped phase. We also explore the
effect of a $\pi/2$ Bragg pulse, causing the increase of the fringe wavelength,
and of a $\pi/2$ rf pulse, revealing the coherent nature of the order parameter
in the spin channel.
