Are microRNAs transcribed from the same DNA strand as their parent messenger RNAs?
The following bear on the question of the relationship of the transcription of microRNAs to that of the pre-mRNAs of protein-coding genes:


Some microRNAs (termed ‘intergenic’) do not reside in a protein-coding gene (e.g. Drosophila mir-31a). Here the question does not arise.





Many (although not all) of those that do reside within a protein-coding gene are found exclusively in introns (termed ‘intronic’) — e.g. mir-11 and mir-998 in Drosophila gene E2f1.





For those microRNAs that reside in a parent gene, the direction of transcription is generally, although not exclusively, the same as that of the transcript (ca. 70%, according to this review).
The question arises whether the intronic microRNAs are generated from the spliced introns of transcripts of their parent genes. One of many papers which consider this is by Ramalingam et al. (2014). It appears that in some cases this may be so, but in other cases this appears to be ruled out by a disparity between the expression profiles of parent genes and microRNAs, and between different microRNAs encoded in the same intron. 
The co-directionality or otherwise of transcription of ‘parent’ mRNA and microRNA has no implications for the interaction of microRNAs with their, often numerous, ‘target’ mRNAs. This is because (1) there is no genetic relationship between parent mRNA and target mRNAs — the parent mRNA, lacking the intron that gave rise to the microRNA, is not the target; (2) the hairpin loop of the microRNA precursor (imperfect though it may be) in effect represents both strands, from which may be generated either the 5ʹ portion, the 3ʹ portion, or both, depending on the microRNA. The miRBase site contains information on relative abundance of 5ʹ- or 3ʹ-fragments for individual microRNAs, and the microrna.org resource lists potential target mRNAs.