Are a meso compound and its mirror image isomers?
meso-compound
A term for the achiral member(s) of a set of diastereoisomers which also includes one or more chiral members.[1, 2]
isomer
One of several species (or molecular entities ) that have the same atomic composition (molecular formula) but different line formulae or different stereochemical formulae and hence different physical and/or chemical properties.[1, 3, 4]

Your notion is correct in so far as the meso-compound and its mirror image are not isomers of each other since they are actually the same compound.
For example, meso-tartaric acid (preferred IUPAC name: (2​R,3​S)-2,3-dihydroxybutanedioic acid) can be superimposed on its mirror image “(2​S,3​R)-2,3-dihydroxybutanedioic acid”; i.e. both structures actually describe the same compound. Thus, they are not isomers of each other. (And hence, “(2​S,3​R)-2,3-dihydroxybutanedioic acid” is not a correct IUPAC name.)
  
However, two further stereochemical configurations are possible, namely (2​R,3​R)-2,3-dihydroxybutanedioic acid and (2​S,3​S)-2,3-dihydroxybutanedioic acid.
  
These structures are non-superimposable mirror images of each other, i.e. they are enantiomers, and the above-mentioned meso-tartaric acid is a diastereomer of both of them.
Therefore, there are a total of three isomers of tartaric acid:

(2​R,3​R)-2,3-dihydroxybutanedioic acid,
(2​S,3​S)-2,3-dihydroxybutanedioic acid, and
the meso-compound (2​R,3​S)-2,3-dihydroxybutanedioic acid.

References
[1] Basic terminology of stereochemistry (IUPAC Recommendations 1996). Pure Appl. Chem. 1996, 68, 2193
[2] meso-compound. In IUPAC Compendium of Chemical Terminology, (Gold Book)
[3] Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994). Pure Appl. Chem. 1994, 66, 1077
[4] isomer. In IUPAC Compendium of Chemical Terminology (Gold Book)