Glass-forming monohydroxy alcohols exhibit two dielectric relaxation signals with super-Arrhenius temperature dependence: a Debye peak and an asymmetrically broadened α-process. We explore the behavior of these distinct relaxation features in mixtures of such liquids by dielectric measurements. The study focuses on the viscous regime of two binary systems: 2-methyl-1-butanol with 2-ethyl-1 hexanol and 1-propanol with 3,7-dimethyl-1-octanol. We find that the logarithmic relaxation time, log(τ), of the Debye peak follows an ideal mixing law (linear change with mole fraction), even in the case of mixing structurally dissimilar components. By contrast, the log(τ) versus mole fraction curve for the α-process is nonlinear, indicative of slower structural relaxation relative to the expectation on the basis of ideal mixing behavior. The latter observation is analogous to the effect of composition on viscosity, heat of mixing, and glass-transition temperature, whereas the ideal mixing of log(τ) seen for the Debye peak is the exception. We conclude that the unusual ideal mixing behavior of dielectric relaxation in monohydroxy alcohols is not a result of structural similarity, but rather yet more evidence of the Debye process being decoupled from other dynamic and thermodynamic properties.