In the spirit of a broad intuition and only pertaining to pre-processing, this article could help make it possible technically: CyTOF workflow: differential discovery in high-throughput high-dimensional cytometry datasets

In the workflow, the package CATALYST now creates an object of class SingleCellExperiment which could theoretically facilitate comparison/integration with scRNA-seq data.

It's certainly a challenge, since you have two different methods, RNA vs. protein-level data, mouse vs. human and a batch effect, all at the same time but you already know that.

As for the CYTOF workflow from that article, in my experience, it required some modifications and didn't cover all pre-processing steps but works well.