Summary We present a novel semiparametric survival model with a log-linear median regression function. As a useful alternative to existing semiparametric models, our large model class has many important practical advantages, including interpretation of the regression parameters via the median and the ability to address heteroscedasticity. We demonstrate that our modeling technique facilitates the ease of prior elicitation and computation for both parametric and semiparametric Bayesian analysis of survival data. We illustrate the advantages of our modeling, as well as model diagnostics, via a reanalysis of a small-cell lung cancer study. Results of our simulation study provide further support for our model in practice.