Abstract The optical properties of BAlN, BGaN and AlGaN ternary alloys are investigated using hybrid density functional for the design of lattice-matched optical structures in the ultraviolet spectrum. The calculated AlGaN properties agree well with previous reports, validating the model. A peculiar non-monotonic behavior of the refractive index as a function of the boron composition is found. The results of this calculation are interpolated to generate a three-dimensional dataset, which can be employed for designing a countless number of lattice-matched and –mismatched heterostructures. These heterostructures could span a range of operating wavelengths well into the deep ultraviolet with refractive indices ranging from 1.98 to 2.41 for AlN at 0 eV and GaN near the GaN bandgap, respectively. An example is shown where a lattice-matched heterostructure, AlN/B_0.108Ga_0.892N, is applied for DBR applications with a large index difference. A DBR comprising the AlN/B_0.108Ga_0.892N heterostructure at the UV wavelength of 375 nm is found to exceed 93% peak reflectivity with only 10 pairs and reaches 100% reflectivity with 35 pairs. For a chosen design with 25 pairs, the DBR has a peak reflectivity of 99.8% and a bandwidth of 26 nm fulfilling the requirements of most devices especially ultraviolet vertical-cavity surface emitting lasers.