Homoromantic

Often, however, asexual people will also identify with a particular sexual orientation, minus the sexual aspect, and may define themselves as heteroromantic, homoromantic, biromantic, transromantic or panromantic.

Source: wiktionary

It does not address other kinds of sexuality such as demisexual (sexual attraction is experienced only when accompanied by a strong emotional attraction), pansexual (attraction across all gender identities and biological sexes. Think “gender blind”), and the romantics (Homoromantic/heteroromantic/aromantic making attraction experienced romantically rather than sexually) among others.

Source: wiktionary

Thus, you can be asexual and biromantic (romantically attracted to men and women), panromantic (romantically attracted to any gender identity), homoromantic (romantically attracted to members of the same sex), or heteroromantic (romantically attracted to members of the opposite sex). Some aces are asexual and aromantic, meaning they enjoy platonic friendships, but don’t experience romantic attraction.

Source: wiktionary

There are different types of ‘aces’, with asexuals being heteroromantic (romantically attracted to the opposite sex); homoromantic (to the same sex); biromantic (to both sexes); panromantic (to both sexes and transsexuals); or aromantic (experiencing little or no romantic attraction to anyone).

Source: wiktionary