Colloidal mesophases are materials that exhibit spontaneous ordering with characteristics between those of crystalline and glassy photonic solids. The study of these partial order photonic mesophases is critical to advancing a new paradigm for photonic structures, with large photonic band gap and negative refraction properties that can be realized via low cost self-assembly. It is well known that photonic crystals dramatically alter the dispersion relations and the spatial power distribution of electromagnetic modes in dielectric materials with a periodic refractive index. Photonic glasses provide control over light diffusion via the optical resonances of building blocks with short-range positional order. New concepts suggest certain types of disorder support photonic band gap properties. This behavior has been predicted in arrangements whose structure factor S(k) tends toward zero as |k| approaches zero including hyperuniform disordered, quasicrystals, and semi-regular tilings. The substitutionally disordered shape-binary phases and single component mesophases, which are the subject of this work, satisfy the structure factor criteria for bandgap formation and their study lies at the frontier of manipulating disorder for colloid-based photonics. Shape-binary mixtures of spheres and peanut-shaped particles (spheres and cut-spheres) are self-organized into substitutionally disordered phases using wedge-cell confinement. The particles are compatible with lobes sizes within ten percent of each other. Particle shape templates are sacrificed to obtain hollow silica shells. This design minimizes segregation between the two particle shape populations by reducing density mismatch. Using fast confocal microscopy, five distinct phases are found between one and two integral layers for the mixture of spheres and peanut-shaped particles: 1(hexagonal) 1β (buckled)  2•(square)  2I (hexagonal)  2II (hexagonal). This sequence is similar to that of single component hard spheres and hard dimers with the addition of major axis orientations for the dimers. For the mixture of spheres and cut-spheres, eight distinct phases are observed: 1_r (hexagonal)  1S_I (side)  1S_II (rotator)  1B (buckled)  2• (square)  2_r (hexagonal)  2S_I (side)  2S_II (rotator). The descriptive sequence is similar to that of pure cut-spheres. The substitutional disorder follows from the Hume-Rothery rules for atomic isomorphous phases. Monte Carlo simulations establish the ideal phases and the phase diagram for the pure dimers and shape mixtures.