If organelles have a membrane, why do nuclei and mitochondria have two membranes?

Nuclei have two membranes because the nuclear envelope is actually and
extension of the ER, so the area between the membranes is
extracellular ER space.  The reason mitochondria have two membranes is
not quite as well understood, but there is a large body of evidence
suggesting that it is due to a phagocytosis.  It is thought that
mitochondria were originally independent organisms that were
phagocytosed by a cell and rather than being destroyed were adopted as
endosymbionts.  Thus, the outer membrane would be a cell membrane
while the inner membrane belongs to the mitochondria.

Mitochondria also use the space between their two membranes (cleverly
named intermembrane space) to create a proton gradient to drive a
pump.  Basically, this space becomes highly acidic, which drives a
protein called ATP-synthase to make lots of ATP.  Having both
membranes is crucial to the functioning of the mitochondria.

For more detailed information, you could look at:

http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/C/CellularRespiration.html

Hope this helps!

Also, the nuclear envelope, which, as zn833 mentioned, is continuous
with the ER space, both surfaces may be needed for nuclear lamins,
which stabilize the structure of the nucleus.

For more detailed info, here are some sources:

http://cellbio.utmb.edu/cellbio/nuclear_envelope.htm
http://www.kcl.ac.uk/kis/schools/life_sciences/biomed/bscb/softcell/ne.html

Hope this helps.

-Jade