The catalytic (heterogeneous) and coupled catalytic-gaseous (hetero-/homogeneous) combustion of fuel-lean hydrogen/air mixtures (equivalence ratio φ = 0.4) in palladium- and rhodium-coated catalytic microchannels was numerically investigated in planar microchannels having a canonical geometry of 10 mm length and 1 mm height. Steady, extinction-induced combustion stability limits were demarcated as a function of inlet velocity and external heat loss at pressures of 1 and 5 bar, with wall thermal conductivities of 1 and 16 W/mK. In each case, interplays between the catalytic and gas-phase chemical reaction pathways, and their impact on the stability limits were identified. The stability results were further compared with literature data for platinum. The simulations indicated that Pd was more resilient against extinction than Rh and had a stronger surface reactivity when competing with gas-phase chemistry in the channel. Similar to Pt, the strong H₂ surface reactivity on Pd resulted in wide stability limits purely determined by surface reactions and independent of gas-phase chemistry. In stark contrast, the presence of gas-phase combustion significantly expanded the stability limits of the Rh channel. The stability limits of Rh at 5 bar were consistently broader than those at 1 bar under all investigated conditions, which was also a behavior different to that of Pd and Pt channels, whose stability limit curves had crossover points between the two pressures. Additional simulations were performed in a Surface Perfectly Stirred Reactor (SPSR), providing comprehensive chemistry information, including sensitivity analyses of key reactions and surface coverages. When approaching extinction, OH(s) was a major surface species on Pd, while the Rh surface was primarily blocked by O(s).