New hybridized discontinuous Galerkin (HDG) methods for the interface problem for elliptic equations are proposed. Unknown functions of our schemes are $$u_h$$ uh in elements and $$\hat{u}_h$$ u^h on inter-element edges. That is, we formulate our schemes without introducing the flux variable. We assume that subdomains $$\Omega _1$$ Ω1 and $$\Omega _2$$ Ω2 are polyhedral domains and that the interface $$\Gamma =\partial \Omega _1\cap \partial \Omega _2$$ Γ=∂Ω1∩∂Ω2 is polyhedral surface or polygon. Moreover, $$\Gamma $$ Γ 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 $$\overline{\Omega }=\overline{\Omega _1\cap \Omega _2}$$ Ω¯=Ω1∩Ω2¯ . Consequently, the solution u of the interface problem may not have a sufficient regularity, say $$u\in H^2(\Omega )$$ u∈H2(Ω) or $$u|_{\Omega _1}\in H^2(\Omega _1)$$ u|Ω1∈H2(Ω1) , $$u|_{\Omega _2}\in H^2(\Omega _2)$$ u|Ω2∈H2(Ω2) . We succeed in deriving optimal order error estimates in an HDG norm and the $$L^2$$ L2 norm under low regularity assumptions of solutions, say $$u|_{\Omega _1}\in H^{1+s}(\Omega _1)$$ u|Ω1∈H1+s(Ω1) and $$u|_{\Omega _2}\in H^{1+s}(\Omega _2)$$ u|Ω2∈H1+s(Ω2) for some $$s\in (1/2,1]$$ s∈(1/2,1] , where $$H^{1+s}$$ H1+s denotes the fractional order Sobolev space. Numerical examples to validate our results are also presented.