Continuous synthesis of formic acid and methyl formate via CO₂ hydrogenation is demonstrated using a molecular iridium complex stably immobilized on a solid covalent triazine framework (CTF) under high-pressure conditions. Compared to formic acid synthesis, methyl formate synthesis is advantageous to enhance the selectivity and yield of formates under kinetically favorable high temperature conditions. Transient in situ vibrational spectroscopy shows that the CTF strongly interacts with CO₂ and H₂, and even activates methanol. Hence, CTF is a promising support for molecular catalysts, even under harsh supercritical and flow conditions, through its strong binding capability.