We investigate the evolution of active galactic nucleus jets on kiloparsec-scales due to their interaction with the clumpy interstellar medium (ISM) of the host galaxy and, subsequently, the surrounding circumgalactic environment. Hydrodynamic simulations of this jet–environment interaction are presented for a range of jet kinetic powers, peak densities of the multiphase ISM, and scale radii of the larger-scale environment – characteristic of either a galaxy cluster or poor group. Synthetic radio images are generated by considering the combination of synchrotron radiation from the jet plasma and free-free absorption from the multiphase ISM. We find that jet propagation is slowed by interactions with a few very dense clouds in the host galaxy ISM, producing asymmetries in lobe length and brightness which persist to scales of tens of kpc for poor group environments. The classification of kiloparsec-scale jets is highly dependent on surface brightness sensitivity and resolution. Our simulations of young active sources can appear as restarted sources, showing double-double lobe morphology, high core prominence (CP > 0.1), and the expected radio spectra for both the inner- and outer-lobe components. We qualitatively reproduce the observed inverse correlation between peak frequency and source size, and find that the peak frequency of the integrated radio spectrum depends on ISM density but not the jet power. Spectral turnover in resolved young radio sources therefore provides a new probe of the ISM.