Generalized Ladner's Theorem
The answer to your question is "yes" for a wide variety of classes and reductions, including logspace reductions and the classes you mentioned, as is proved in these papers:


  H. Vollmer.  The gap-language technique revisited.  Computer Science Logic, Lecture Notes in Computer Science Vol. 533, pages 389-399, 1990.
  
  K. Regan and H. Vollmer.  Gap-languages and log-time complexity classes.  Theoretical Computer Science, 188(1-2):101-116, 1997.


(You can download gzipped postscript files of these papers here.)

The proofs follow the basic principle of Uwe Schöning's extension of Ladner's theorem:


  Uwe Schöning.  A uniform approach to obtain diagonal sets in complexity classes.  Theoretical Computer Science 18(1):95-103, 1982.


Schöning's proof has always been my favorite proof of Ladner's theorem -- it's both simple and general.