Arctic delta channel dynamics and coastal deposition patterns are uniquely affected by ice and permafrost. Building on previous experiments that documented the individual effects of ice and permafrost, we conducted new numerical modeling experiments to examine the combined influences of ice thickness and permafrost erodibility. We quantified the effects of ice, permafrost, and their combination on channel migration, avulsion, and persistence; onshore and nearshore deposition; and large‐scale delta morphology. Both ice and permafrost limited channel mobility, enhanced overbank deposition, and roughened shorelines. Thick ice increased offshore channel incision and sediment delivery. Permafrost stabilized channels and focused deposition that led to enhanced channel levee development. The increased levee deposition limited widespread channel infilling leading to the preservation of abandoned channels. Levee growth was enhanced by overbank flooding due to ice‐driven changes in water surface elevations. This flooding led to more extensive levees on deltas with both ice and permafrost compared to deltas with only permafrost. Ice also preserved small channels, leading to size‐dependent channel persistence: the presence of ice in the channels reduced the fraction of time small channels remained active relative to larger channels. Resistant permafrost damped this effect, as smaller and more distal channels were active earlier in the flood on deltas with resistant permafrost likely due to the smaller number of channels on permafrost‐laden deltas. Finally, our results suggest that the loss of both ice and permafrost will increase channel mobility, decrease overbank flooding, increase shoreline progradation rates, and decrease offshore transport of riverine fluxes.