Cassiopea andromeda (Forsskål, 1775), commonly found across the Indo-Pacific Ocean, the Red Sea, and now also in the warmest areas of the Mediterranean Sea, is a scyphozoan jellyfish that hosts autotrophic dinoflagellate symbionts (family Symbiodiniaceae). Besides supplying photosynthates to their host, these microalgae are known to produce bioactive compounds as long-chain unsaturated fatty acids, polyphenols, and pigments, including carotenoids, with antioxidant properties and other beneficial biological activities. By the present study, a fractionation method was applied on the hydroalcoholic extract from two main body parts (oral arms and umbrella) of the jellyfish holobiont to obtain an improved biochemical characterization of the obtained fractions from the two body parts. The composition of each fraction (i.e., proteins, phenols, fatty acids, and pigments) as well as the associated antioxidant activity were analyzed. The oral arms proved richer in zooxanthellae and pigments than the umbrella. The applied fractionation method was effective in separating pigments and fatty acids into a lipophilic fraction from proteins and pigment–protein complexes. Therefore, the C. andromeda–dinoflagellate holobiont might be considered as a promising natural source of multiple bioactive compounds produced through mixotrophic metabolism, which are of interest for a wide range of biotechnological applications.