The chemical identity and integrity of the genome is challenged by the incorporation of ribonucleoside triphosphates (rNTPs) in place of deoxyribonucleoside triphosphates (dNTPs) during replication. Misincorporation is limited by the selectivity of DNA replicases. We show that accumulation of ribonucleoside monophosphates (rNMPs) in the genome causes replication stress and has toxic consequences, particularly in the absence of RNase H1 and RNase H2, which remove rNMPs. We demonstrate that postreplication repair (PRR) pathways—MMS2-dependent template switch and Pol ζ-dependent bypass—are crucial for tolerating the presence of rNMPs in the chromosomes; indeed, we show that Pol ζ efficiently replicates over 1–4 rNMPs. Moreover, cells lacking RNase H accumulate mono- and polyubiquitylated PCNA and have a constitutively activated PRR. Our findings describe a crucial function for RNase H1, RNase H2, template switch, and translesion DNA synthesis in overcoming rNTPs misincorporated during DNA replication, and may be relevant for the pathogenesis of Aicardi-Goutières syndrome.