In this work, we investigated for the first time hydrophobic deep eutectic solvents (DES) as supported liquid membrane (SLM) for electromembrane extraction (EME). Camphor, coumarin, DL-menthol, and thymol were used as non-ionic DES components. Different DESs compositions were tested, to study systematically the importance of hydrogen bonding and dispersion/aromatic interactions during mass transfer across the SLM. Unexpectedly, mixtures of coumarin and thymol were highly efficient SLMs, and provided exhaustive or near-exhaustive extraction of non-polar bases, non-polar acids, and polar bases. SLMs with such performance for both bases and acids, in a large polarity window, are not found in current literature. The SLMs were highly aromatic, very strong hydrogen bonding donors, and moderately strong hydrogen bonding acceptors. Aromatic (π type) interactions were apparently very important for transfer of bases, while hydrogen bonding were dominant for acids. EME of six polar basic drugs from plasma, with a coumarin and thymol mixture as SLM, and combined with UHPLC-MS/MS analysis, was evaluated to test the potential for analytical applications. Plasma was diluted 1:1 with phosphate buffer pH 2.0. Calibration curves were linear in the therapeutic ranges (0.970 < R² < 0.999), recoveries ranged between 47 and 93%, and repeatability was within 1.6–10.7% RSD. The clean-up efficiency was excellent and no matrix effects from plasma were seen. Presence of trace levels of coumarin in the acceptor phase was however found to cause some ion enhancement. Based on the current work, we foresee more research on the use of DES in EME.