Monosexism is a belief that monosexuality (either exclusive heterosexuality and/or homosexuality) is superior to or more legitimate than a bisexual or other non-monosexual orientation. It is generally used to describe instances of discrimination against bisexual/non-monosexual people which are less violent or overt than biphobia.
Specifically, monosexism promotes exclusive gynephilia and androphilia, regardless of the sex of the person.
Some heterosexual people define bisexuality as morally wrong, as sinful or as dangerous, while some go further, describing all orientations other than heterosexual as such. Some homosexual men dismiss self-identified bisexual men as lacking in self-acceptance, and claim that such men are actually gay but are in denial. Lesbians who make dismissive claims about the behavior of self-identified bisexual women tend to state that such women are actually heterosexual, and are engaging sexually with other women for attention from men, or out of confusion. Some people, regardless of their own orientation, dismiss bisexual/non-monosexual people as merely promiscuous. Many bisexual/non-monosexual people have some form of internalized monosexism, or feeling that their own sexual orientation is illegitimate, which they have to work through.
Monosexism refers to prejudice against bisexuality specifically. While it describes a view of the superiority of heterosexuality and homosexuality, it is not the same as heterosexism or homosexism which are views that include each's superiority to the other.