The epitranscriptome embodies many new and largely unexplored functions of RNA. A major roadblock in the epitranscriptomics field is the lack of transcriptome-wide methods to detect more than a single RNA modification type at a time, identify RNA modifications in individual molecules, and estimate modification stoichiometry accurately. We address these issues with CHEUI (CH3 (methylation) Estimation Using Ionic current), a new method that concurrently detects N6-methyladenosine (m6A) and 5-methylcytidine (m5C) in individual RNA molecules from the same sample, as well as differential methylation between any two conditions. CHEUI processes observed and expected nanopore direct RNA sequencing signals with convolutional neural networks to achieve high single-molecule accuracy and outperform other methods in detecting m6A and m5C sites and quantifying their stoichiometry. CHEUI’s unique capability to identify two modification types in the same sample reveals a non-random co-occurrence of m6A and m5C in mRNA transcripts in cell lines and tissues. We further combined CHEUI's predictions with ribosome profiling to identify specific combinations of m6A and m5C that were associated with enhanced or depleted mRNA translation efficiency. CHEUI unlocks an unprecedented potential to study RNA modification configurations and discover new epitranscriptome functions.