We aim to review the spectral synthesis technique to derive the stellar atmospheric parameters (Teff, log g, and [Fe/H]) of 348 M dwarfs in light of the optical and near-infrared spectra obtained with CARMENES, the high-resolution, double-channel spectrograph installed at the 3.5 m telescope at the Calar Alto observatory (Spain). The analysis relies on the SteParSyn code as the preferred MCMC implementation of the spectral synthesis technique, along with 75 carefully selected, magnetically insensitive, Fe I and Ti I lines plus the γ- and ϵ-TiO bands synthesised with a grid of BT-Settl model atmospheres and the turbospectrum code. To avoid potential degeneracies in the parameter space, we impose a Bayesian prior on Teff and log g based on comprehensive, multi-band photometric data available for the sample. As a benchmark test in Teff, log g, and [Fe/H] we place special emphasis on three special subsets in our sample, namely 14 M dwarfs with interferometric angular diameter measurements, 15 M+M systems, and 7 wide physical binaries harbouring an FGK-type primary with known metallicity.