Within psychiatry, how is homosexuality discussed or classified?
In 1973, the American Psychiatric Association (APA) removed the diagnosis of “homosexuality” from the second edition of its Diagnostic and Statistical Manual (DSM) (Jack Drescher, 2015).

Theories of pathology which declared that some internal defect or external pathogenic agent causes homosexuality, have been rejected, such as the theories of immaturity which considered the homosexuality a "developmental arrest".

It is rare to find a theory of homosexuality that does not draw upon gender beliefs that contain implicit cultural ideas about the “essential” qualities of men and women. 
Who is a real man? Who is a real woman? 
Since there weren't scientific evidences to claim: "Homosexuality is a mental disorder", after a vote, Homosexuality has been depathologized.

Accordingly, the answer to your question is no. Homosexuality is not a mental disorder, it's just a normal sexual orientation.

For further informations i suggest: "Out of DSM: Depathologizing Homosexuality" (Jack Drescher) 2015 : LINK: 

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4695779/