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Disk diffusion tests are employed to determine the susceptibility of bacteria to antibiotics by measuring the zone diameter (ZD) of inhibition. Previous work suggested to use a composite model when modeling minimum inhibitory concentration measurements. This model combines a parametric distribution covering the range of observations from the susceptible component with a non-parametric distribution capturing the range of observations containing also resistant observations. We investigate the use of this model for ZD data and also consider a two-component mixture model combining the parametric distribution with the non-parametric distribution relaxing the split of the support for both distributions. We present maximum likelihood and penalized maximum likelihood estimation of both models using a normal or a skew-normal distribution as parametric distribution while taking the restricted support and the rounding of the data into account. We illustrate the use of these models in a simulation study on artificial data and on data available from the web page of the European Committee on Antimicrobial Susceptibility Testing (EUCAST).