A new aromatic diiodide monomer, bis(4-(3-iodophenoxy)phenyl)phenylphosphine oxide (BIPPO), was prepared by condensation of bis(4-fluorophenyl)phenylphosphine oxide with 3-iodophenol. A series of poly(arylene ether amide triphenylphosphine oxide)s were synthesized via heterogeneous palladium-catalyzed carbonylative polycondensation of BIPPO, aromatic diamines, and carbon monoxide. Polymerization reaction proceeded smoothly in N,N-dimethylacetamide (DMAc) at 120 °C with 1,8-diazabicyclo[5,4,0]-7-undecene (DBU) as the base by using the bidentate phosphino-modified magnetic nanoparticles-anchored palladium complex [2P-Fe3O4@SiO2-PdCl2] as a recyclable catalyst under 1 bar of CO, producing new poly(arylene ether amide triphenylphosphine oxide)s with inherent viscosities ranging from 0.69 to 0.76 dl/g. All the polymers obtained were easily soluble in strong polar aprotic organic solvents and even in less polar pyridine at room temperature, and provided transparent, flexible and tough films by casting from their DMAc solutions. These polymers displayed good thermal stability with the glass transition temperatures ranging from 196 to 249 °C, the temperatures at 5% weight loss ranging from 441 to 490 °C in nitrogen. All the polymers were amorphous and their films showed good mechanical behavior with tensile strengths of 78.5–91.6 MPa, tensile moduli of 2.15–2.69 GPa, and elongations at break of 9.8–14.6%.