The term “identical twins” is generally used as a synonym for “monozygotic (MZ) twins.” Both terms assume that that the twins developed from the same fertilized egg (zygote), have identical DNA, and therefore look identical. But, as explained here, identical twins do not always look exactly the same. And male/female twins certainly don’t look identical!
So let’s rephrase the question: Can a male/female twin pair be MZ twins?
The term “MZ twins” simply means that the twins came from the same zygote. Using that definition, the answer is yes! In extremely rare cases, MZ twins that began as a male zygote have developed into a male/female twin pair!
Humans have 23 pairs of chromosome. One of these pairs of chromosomes, called the sex chromosomes (X and Y), determine the sex of the person. Females have two X chromosomes (XX) and males have one X and one Y chromosome (XY). Very rarely, a glitch in copying sex chromosomes can occur, either during the formation of sperm or egg cells, or during the divisions of the zygote after it is formed. The result can be a MZ twin pair of opposite sexes. Below are two possible examples of how this could happen. Remember this is an extremely rare event – only a few cases of MZ twins of opposite sexes have been reported in the medical literature.
First example: After a male (XY) zygote is formed, it starts to develop and split into two embryos. Early in this process, inaccurate copying of the sex chromosomes could result in the loss of the Y chromosome in some cells. The embryo that is formed from the cells missing the Y chromosome would develop into a female (XO). The other embryo would still develop into a male (XY). The twin with only one X chromosome would be female but her cells would have only one copy of the X chromosome. This condition is called Turner Syndrome.
Second example: There could be a glitch in copying sex chromosomes during the formation of sperm or egg cells, resulting in a male zygote that starts out with an extra X chromosome (XXY). Through a complicated series of events, this zygote could result in the birth of MZ twins who are XY (male) and XX (female).
After birth, if one member of a pair of MZ twins had a sex change operation, that would also result in a pair of opposite sex MZ twins.
So, while there is a tiny possibility that a male/female pair of twins could be MZ, it is highly unlikely. It is safe to assume that just about all male/female twin pairs are DZ twins.
References
Machin G. 2009. Non-identical monozygotic twins, intermediate twin types, zygosity testing, and the non-random nature of monozygotic twinning: A review. Am J Med Genet Part C Semin Med Genet 151C:110–127.
Zech, N. H., Wisser, J., Natalucci, G., Riegel, M., Baumer, A. and Schinzel, A. (2008), Monochorionic-diamniotic twins discordant in gender from a naturally conceived pregnancy through postzygotic sex chromosome loss in a 47,XXY zygote. Prenat. Diagn., 28: 759–763. doi: 10.1002/pd.2031