New hybridized discontinuous Galerkin (HDG) methods for the interface problem for elliptic equations are proposed. Unknown functions of our schemes are (Formula presented.) in elements and (Formula presented.) on inter-element edges. That is, we formulate our schemes without introducing the flux variable. We assume that subdomains (Formula presented.) and (Formula presented.) are polyhedral domains and that the interface (Formula presented.) is polyhedral surface or polygon. Moreover, (Formula presented.) is assumed to be expressed as the union of edges of some elements. We deal with the case where the interface is transversely connected with the boundary of the whole domain (Formula presented.). Consequently, the solution u of the interface problem may not have a sufficient regularity, say (Formula presented.) or (Formula presented.), (Formula presented.). We succeed in deriving optimal order error estimates in an HDG norm and the (Formula presented.) norm under low regularity assumptions of solutions, say (Formula presented.) and (Formula presented.) for some (Formula presented.), where (Formula presented.) denotes the fractional order Sobolev space. Numerical examples to validate our results are also presented.