I'm working on a very similar problem. I just recently discovered PLS after struggling with canonical correlation. I suggest you check out the plsdepot package in R, the plsreg2() function seems to do exactly this task.
As far as workflow, the data should be properly normalized (whether you're using microarray or RNAseq). This makes sense because there are confounding variables unique to gene expression analysis that must be controlled for (e.g. chip background or library size). Scaling apparently isn't as much of an issue, because PLS doesn't assume you have a multivariate normal joint distribution (but I prefer to do it anyway), however, plsreg2() automatically z-scales (standardizes) the data anyway. Assessing your model should be done with care, I recently attempted to explain why in another post here. Lastly, this is a link to the article that first tipped me off to this package.
Preferential association with latent variables is what should enable us to assign genes/miRNAs to groups (and predict their interaction), by assessing how well each set of latent variables explain predictor/response variance. The final step would be to perform statistical tests to determine which variables are significantly associated with each latent variable. I posted citations below to the only examples I could find detailing a method using PLS to investigate miRNA-mRNA interactions.
BMC Medical Genomics 2011, 4:44 doi:10.1186/1755-8794-4-44
Bioinformatics (2002) 18 (1): 39-50.
Best of luck, let me know if you figure out the significance tests because I'm still working on my own analysis!