In this work, we employ a simple two-step growth technique to deposit impurity doped heteroepitaxial thin films of (0001) ZnO onto (111) MgAl2O4 spinel substrates through a combination of atomic layer deposition (ALD) and hydrothermal growth. The hydrothermal layer is doped with Al, Ga, and In through the addition of their respective nitrate salts. We evaluated the effect that varying the concentrations of these dopants has on both the structural and optical properties of these films. It was found that the epitaxial ALD layer created a ⟨111⟩MgAl2O4∥⟨0001⟩ZnO out-of-plane orientation and a ⟨1¯1¯2⟩MgAl2O4∥∥⟨011¯0⟩ZnO in-plane orientation between the film and substrate. The rocking curve line widths ranged between 0.75° and 1.80° depending on dopant concentration. The optical bandgap determined through the Tauc method was between 3.28 eV and 3.39 eV and showed a Burstein-Moss shift with increasing dopant concentration.