The main difference between mRNA and miRNA is in the reverse transcription since in the TaqMan system every miRNA requires a unique stem-loop primer. To the best of my knowledge the real-time PCR can be the same as it follows the amplification-dependent release of FAM fluorescence from its quencher relative to the constant reference ROX dye in the reaction. There is a mild dependency on amplicon length, but TaqMan probes for both mRNAs and miRNAs are supposed to generate similar amplicon lengths.
As a side note, if you use a method based on artificial polyadenylation followed by universal-tag-oligo-dT-driven reverse transcription, you can use the much much much cheaper option of SYBR Green in combination with plain oligos for both miRNAs and mRNAs from the same RT - no worrying about different RT efficiencies! If you are only looking at a few genes, go with TaqMan, but if you are planning more than, say, 10 types of probes, the cost gradient can be about 100-fold! The downside is that you have to include more controls. Which is also the upside :-) Let me know if you want a protocol.