  Type IIB superstring theory has AdS_3 x S^3 x M_4 (where the manifold M_4 is
either K_3 or T^4) solutions which preserve sixteen supersymmetries. In this
paper we consider half-BPS solutions which are locally asymptotic to AdS_3 x
S^3 x M_4 and preserve eight of the sixteen supersymmetries. We reduce the BPS
equations and the Bianchi identity for the self-dual five-form field to a set
of four differential equations. The complete local solution can be
parameterized in terms of two harmonic and two holomorphic functions and all
bosonic fields have explicit expressions in terms of these functions.
  We analyze the conditions for global regularity and construct new half-BPS
Janus-solutions which have two asymptotic AdS_3 regions. In addition, our
analysis proves the global regularity of a class of solutions with more than
two asymptotic AdS_3 regions. Finally, we discuss the dual interpretation as a
supersymmetric interface theory for the half-BPS Janus solutions carrying only
Ramond-Ramond three-form charge.
