In this paper, we study the excitonic linewidths and peak energies in two transition metal dichalcogenide heterostructures of MoWSe and its binary counterparts, MoSe and WSe. We observe spectra composed of several individual excitonic transitions in temperature-dependent photoluminescence measurements. Among these are transitions of neutral excitons and trions from the binary layers and the interlayer excitons from the heterostructures. The luminescence linewidth of the interlayer excitons is significantly broader than the linewidths of the excitonic transitions from the binary layers. We attribute this additional line broadening to dielectric disorder caused by spatial inhomogeneity at the interface.