UV-induced degradation and parasitic ultraviolet (UV) absorption by the "sun-facing" carrier transport layer in a perovskite cell hinders stability and electrical performance when the perovskite cell is a top cell for a Si-based tandem. In this work, we tackle these issues by applying textured polydimethylsiloxane (PDMS) films that incorporate a down-shifting material (Ba,Sr)2SiO4:Eu2+ micron phosphor on the front of monolithic perovskite/silicon tandem cells. This film serves multiple purposes: antireflective control for the top cell, light trapping in the Si cell, as well as absorbing UV and re-emitting green light with high quantum yield. When applied onto a 4 cm2 monolithic perovskite/silicon tandem solar cell, the power conversion efficiency was improved from 20.1% (baseline device without any antireflective film) to 22.3% (device with an antireflective film but without the phosphors) and to 23.1% (device with down-shifting phosphor-incorprated antireflective film). The steady-state efficiency of 23.0% and a high fill factor (FF) of 81% achieved by the champion device are the highest values to date for a monolithic perovskite/silicon tandem that uses a homojunction silicon bottom cell. Moreover, results of a continuous UV irradiation test show that this composite down-shifting antireflection film significantly enhances the UV stability for the tandem device. This work demonstrates an elegant approach for improving the efficiency and stability for larger-area perovskite/silicon tandems.