Your question has been answered on Java page:
you will need to install both 32-bit and 64-bit Java in order to have the Java plug-in for both browsers.
If you have 64-bit Windows, you have two IE versions, 32-bit and 64-bit.
"C:\Program Files (x86)\Internet Explorer\iexplore.exe"
Internet Explorer (64-bit)
"C:\Program Files\Internet Explorer\iexplore.exe"
The first one runs IE from the "Program Files (x86)" folder, this is the 32-bit version. The second one is the 64-bit version.