Do stairs need to be the same height after landing?
According to the International Residential Code (IRC), the 3/8" variance only applies to a "flight of stairs" not the entire "stairway".


  International Residential Code 2009
  
  Chapter 3 - Building Planning
  
  Section 311 Means of Egress
  
  R311.7 Stairways.  
  
  R311.7.4.1 Riser height. The maximum riser height shall be 73/4 inches (196 mm). The riser shall be measured vertically between leading edges of the adjacent treads. The greatest riser height within any flight of stairs shall not exceed the smallest by more than 3/8 inch (9.5 mm).


Looking at the definition of stairway and flight, you can see that the the 3/8" variance only applies to individual flights of stairs, and not the entire stairway. 


  Chapter 2 - Definitions
  
  Section 202 Definitions
  
  Stairway. One or more flights of stairs, either exterior or interior, with the necessary landings and 
  platforms connecting them, to form a continuous and uninterrupted passage from one level to another.
  
  Flight. A continuous run of rectangular treads or winders or combination thereof from one landing to another.


However, you may find that changing the riser height by too much within a stairway could lead to a tripping hazard.  As you travel up/down the stairs, your body gets used to the step height.  If midway through the stairway the step height changes, you may become temporarily disoriented and potentially trip or misstep.