Rosemary (Rosmarinus officinalis) is a natural source of bioactive compounds that have high antioxidant activity. It has been in use as a medicinal herb since ancient times, and it currently is in widespread use due to its inherent pharmacological and therapeutic potential, in the pharmaceutical, food, and cosmetic industries. Natural deep eutectic systems (NADESs) have recently been considered as suitable extraction solvents for bioactive compounds, with high solvent power, low toxicity, biodegradability, and low environmental impact. The present work concerns the extraction of compounds such as rosmarinic acid, carnosol, carnosic acid, and caffeic acid, from rosemary using NADESs. This extraction was carried out using heat and stirring (HS) and ultrasound-assisted extraction (UAE). A NADES composed of menthol and lauric acid at a molar ratio of 2:1 (Me:Lau) extracted carnosic acid and carnosol preferentially, showing that this NADES exhibits selectivity for nonpolar compounds. On the other hand, a system of lactic acid and glucose (LA:Glu (5:1)) extracted preferentially rosmaniric acid, which is a more polar compound. Taking advantage of the different polarities of these NADESs, a simultaneous extraction was carried out, where the two NADESs form a biphasic system. The system LA:Glu (5:1)/Men:Lau (2:1) presented the most promising results, reaching 1.00 ± 0.12 mg of rosmarinic acid/g rosemary and 0.26 ± 0.04 mg caffeic acid/g rosemary in the more polar phase and 2.30 ± 0.18 mg of carnosol/g of rosemary and 17.54 ± 1.88 mg carnosic acid/g rosemary in the nonpolar phase. This work reveals that is possible to use two different systems at the same time and extract different compounds in a single-step process under the same conditions. NADESs are also reported to stabilize bioactive compounds, due to their interactions established with NADES components. To determine the stability of the extracts over time, the compounds of interest were quantified by HPLC at different time points. This allows the conclusion that bioactive compounds from rosemary were stable in NADESs for long periods of time; in particular, carnosic acid presented a decrease of only 25% in its antioxidant activity after 3 months, whereas the carnosic acid extracted and kept in the methanol was no longer detected after 15 days. The stabilizing ability of NADESs to extract phenolic/bioactive compounds shows a great promise for future industrial applications.