The interface is an atomic plane; it will hardly offer any resistance to an electron motion perpendicular to this plane! But, there is inevitably a Schottky barrier at any semiconductor/electrode region. The Schottky barrier is not characterised by a resistance, but, by a barrier height. The Schottky barrier height can de extracted from the I-V, and/or C-V, and/or internal photo-emission characteristics.
The Schottky barrier is a junction and has the diode characteristics.
As has already been said, there are linear and non-linear parts associated with the I-V of the diode (assuming that the current is homogeneous - which is another story).
Whether there is a 'contact resistance' component depends on the technology used to make the diode. Often there is a thin native oxide layer between metal and s/c and this will present probably insignificant 'resistance' as it is so thin that charge easily tunnels through. Such a layer however, will influence the barrier height associated with the exponential part of the transport (the non-linear bit).
Most of the series-R (easily extracted form an I-V plot), is due to the bulk semiconductor and back ohmic contact - which will also have a well-defined 'contact resistance.'
Plenty of good text books to describe what's happening including those by Rhoderick or Sze. The inhomogeneous effects are described thoroughly by RT Tung's papers.