Is "monosexual" still a valid term in biology?
I suspect "monosexual" is a term recruited in sociology, psychology and/or medicine. I haven't ever heard of it in application to biological questions. It's a behavioral habit and doesn't seem to be directly related to the (biological) opposition "separate sexes" vs "hermaphroditism".

In biology:

Animals can either be gonochoristic (separate sexes) or hermaphroditic. If an animal species reproduces without gametes it's called asexual (in animals asexual reproduction is rarely the only way of propagation), and if only females are present which give birth without fertilization, they are called parthenogenetic.

In some cases different modes of reproduction are utilized by different stages (alternate generations) or even phases (larva vs adult, young vs old). In other cases in populations coexist males and hermaphrodites or males and parthenogenetic females. 

Mammals, including humans, are (nearly) perfect examples of gonochoristic animals: only a male and a female together can produce offspring. If someone is homosexual (it refers to behavior only), he is a dead end in this respect.