A biorefinery process was developed to isolate phycobiliproteins, sulfated polysaccharides, and phenolic compounds from Palmaria palmata. The extraction process was carried out in three stages using ultrasound-assisted extraction (UAE) and pressurized liquid extraction (PLE) integrated with different natural deep eutectic solvents (NaDESs). In general, PLE provided higher phycobiliprotein contents than UAE in the first step of the process. In fact, the hydrolysis product of the PLE-NaDES extracts achieved a higher antioxidant capacity than that of the UAE-NaDES extracts. Particularly, glycerol:glucose (2:1) with 50% water in combination with PLE was the most suitable NaDES to recover the highest phycobiliprotein, protein, and sulfated polysaccharide contents from Palmaria palmata in the first and second steps of the biorefinery process. Finally, a PLE-NaDES using choline chloride:glycerol (1:2) with 60% water as the NaDES was employed for the recovery of antioxidant and neuroprotective phenolic compounds from the residue of the second step, obtaining a higher total phenolic content than employing PLE with ethanol/water (70:30, v/v) as the extraction solvent. Moreover, a forced stability study revealed that the NaDESs provided a protective effect compared to the water extracts against the degradation of phycobiliproteins, preserving their color over time. This study contributes to the recovery of high-value components from an undervalued biomarine source through a sustainable biorefinery process.