Marine macroalgae (seaweed) are an excellent source of novel bioactive metabolites. The biorefinery concept applied to seaweed facilitates the extraction of many chemical constituents from the same biomass ensuring that the resource is used fully, generating few residues through a succession of extraction steps. In the present study, the biomass of the carragenophyte Solieria filiformis (Rhodophyta, Gigartinales) cultured in an integrated multi-trophic aquaculture (IMTA) system was evaluated to obtain valuable products by a biorefinery approach. Enzymatic-assisted extraction (EAE) and microwave-assisted extraction (MAE) were the eco-friendly technologies used to ensure an environmentally friendly valorization of the biomass. Three valuable products were successfully recovered: a water-soluble extract rich in proteins and sulfated polysaccharides suitable as a food supplement; a lipid fraction rich in polyunsaturated fatty acids (PUFAs) with potential to be used in the nutraceutical industry; and a pure ι-carrageenan with a powerful antiviral activity against Herpes simplex virus (EC50 = 6.3 µg mL−1) comparable to the commercial antiviral acyclovir (EC50 = 3.2–5.4 µg mL−1).