Abstract: In contrast to classical knots, the knot type of a genus two handlebody-knot is not determined by its exterior, and it is often a challenging task to distinguish handlebody-knots with homeomorphic exteriors. The present paper considers an invariant (the annulus diagram), defined via Johannson’s characteristic submanifold theory and the Koda–Ozawa classification for essential annuli, and demonstrates its capability to distinguish such handlebody-knots; particularly, the annulus diagram is able to differentiate members in the handlebody-knot families given by Motto and Lee–Lee.